Deformational Structures on Smooth Manifolds

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Effects of deformation on the electronic properties of B–C–N nanotubes

Effects of deformation on the electronic properties of B–C–N nanotubesS.Azevedo a,n,A.Rosas a,M.Machado b,J.R.Kaschny c,H.Chacham da Departamento de Fı´sica,Universidade Federal da Paraı´ba,Caixa Postal5008,58059-900Jo~ao Pessoa—PB,Brazilb Departamento de Fı´sica,Universidade Federal de Pelotas,Caixa Postal354,96010-900Pelotas—RS,Brazilc Instituto Federal da Bahia—Campus Vito´ria da Conquista,Av.Amazonas3150,45030-220Vito´ria da Conquista—BA,Brazild Departamento de Fı´sica,ICEX,Universidade Federal de Minas Gerais,Caixa Postal702,30123-970Belo Horizonte—MG,Brazila r t i c l e i n f oArticle history:Received12April2012Received in revised form19July2012Accepted5August2012Available online16August2012Keywords:DeformationElectronic structureNanotubesa b s t r a c tWe applyﬁrst-principles methods,using density functional theory,to investigate the effects ofﬂattening deformation on the electronic properties of BC2N and C-doped BNNTs.Four different typesof BC2N structures are considered.Two of them are semiconductors,and the radial compressionproduces a signiﬁcant reduction of the energy band gap.The other two types of structures are metallic,and the effect of radial compression is quite distinct.For one of them it is found the opening of a smallband gap,and for the other one no changes are observed.For C-doped tubes,it is also found that theelectronic properties undergo signiﬁcant modiﬁcations when subjected to radial compression.&2012Elsevier Inc.All rights reserved.1.IntroductionAlong the last two decades,planar and curved carbon nanos-tructures,which the best examples are graphene,fullerenes andcarbon nanotubes(CNTs),have been subject of strong scientiﬁcand technological attention due to their innovative properties.Depending on their geometry,CNTs can be either a semiconduct-ing or a metallic nanostructured material,while bulk graphitebehaves as a semi-metal[1,2].The complete replacement ofcarbon in the CNT structure,by alternating boron and nitrogenatoms,leads to the formation of boron nitride nanotubes(BNNTs)with quite different electronic properties when compared withcarbon ones[3,4].Such nanostructured material is a wide gapsemiconductor with optical band gap around 5.8eV which isalmost independent of the tube chirality[5].Nevertheless,theirelectronic behavior can be signiﬁcantly modiﬁed by the presenceof defects,especially when substitutional dopants are incorpo-rated into the honeycomb structure.Schmidt et al.show theore-tically that the introduction of substitutional C impurities in aBNNT structure induces signiﬁcant reduction of the formationenergy when compared to other types of native defects[6].Wuet al.,usingﬁrst-principles calculations,found that substitutionalC atoms can produce spontaneous magnetization[7].In anyway,these results demonstrate that substitutional C defects play animportant role in the electronic behavior of BNNTs,indicating aneffective method for tunning their electronic properties.The structural similarity between graphene and hexagonal BNstructures has motivated many efforts towards the developmentB–C–N alloys.In the past,B–C–N thinﬁlms with differentchemical compositions were prepared by chemical vapor deposi-tion(CVD)using BCl3,N2,H2,CCl4or even acetylene(C2H2)asstarting compounds[12–14].Such thinﬁlms were characterizedas semiconductors,having graphite-like layered structures withdistinct band gap energies for different stoichiometries[15,16].Concerning nanostructured materials,B–C–N nanotubes havebeen synthesized by electrical arc discharge[20,21],pyrolysis[22],laser ablation[23],and more recently by laser vaporization[24],motivating a large number of theoretical investigations[25–31].It is expected that the electronic behavior of such hybridstructures could be intermediate between those found for CNTsand BNNTs,showing different properties for each stoichiometry.Therefore,controlling their composition during synthesis it couldbe possible to obtain nanomaterials with speciﬁc properties,appropriated to the development of upcoming nanodevicetechnologies.In addition to doping,stoichiometric manipulations and defectengineering,it is well known that structural deformation inducesigniﬁcant modiﬁcations on the electronic properties of nanoma-terials.Such changes in the electronic behavior of the nanostruc-tures,due to mechanical tension,torsion andﬂattening,are ofgreat interest for the design of nanodevices and innovativenanosensors.First principles calculations have been widely usedto investigate the effects of deformation on the electronic proper-ties of CNTs[32–34].Mazzoni and Chacham found that theContents lists available at SciVerse ScienceDirectjournal homepage:/locate/jsscJournal of Solid State Chemistry0022-4596/$-see front matter&2012Elsevier Inc.All rights reserved./10.1016/j.jssc.2012.08.008n Corresponding author.E-mail addresses:sazevedo@ﬁsica.ufpb.br,s_azevedo2003@.br(S.Azevedo).Journal of Solid State Chemistry197(2013)254–260ﬂattening deformation produce a systematical reduction of the band gap energy,from0.92eV to zero[32].In addition,supposing an interaction of a scanning microscope tip with a typical carbon nanotube,they estimated that the applied force per unit length to reach a semiconductor–metal transition should be about 7N/m.Such results are consistent with recent experiments which demonstrate an insulator to metal transition in com-pressed CNTs[35].Detailed theoretical investigations were also done for BNNTs [36–39].For example,Kinoshita et al.found that for single-walled boron nitride nanotubes the energy of the conduction band minimum decreases with the increasingﬂattening deformation, while the energy of the valence band hardly changes[36].In general,it is possible to see from such results that the inﬂuence of theﬂattening distortion on the gap energy of a BN tube is smaller when compared to the one found for CNTs.Similar studies were performed for other types of nanomaterials.However little information can be found about the effects of mechanical defor-mation on the properties of B–C–N nanostructures and doped BNNTs.Therefore,in order toﬁnd more information about such open points,we present a theoretical study about the effects of ﬂattening deformations on the structural and electronic proper-ties of BC2N nanotubes and C-doped(10,0)BNNTs on the basis of ﬁrst-principles calculations.2.Calculation detailsThe calculation method is based on the density functional theory(DFT)[40]as implemented in the SIESTA code[41].We use norm-conserving Troullier Martins pseudopotential[42]in the Kleinman–Bylander factorized form[43],and a double-z basis set composed of numerical atomic orbitals ofﬁnite range.Polariza-tion orbitals are included for all atoms,and we make use of the generalized gradient approximation(GGA)for the exchange-correlation potential[44].All the geometries are fully relaxed, with residual forces smaller than0.1eV/˚A.Flattened BC2N relaxed supercells are shown in Fig.1a–d.As indicated,four types of tubular structures have been constructed using a similar procedure as described elsewhere[25].Each structure presents a distinct atomic arrangement,named model I,II,III and IV which corresponds to the initial state of the ones shown in Fig.1a–d.These structures have been constructed from graphene-like BC2N arrangements,previously investigated on Ref.[30],alternating BN and graphene stripes along the zigzag direc-tion.The stripes are perpendicular to the tube axis on models I and II,and parallel to such axis on models III and IV.It is worth mentioning that the uncompressed nanotubes corresponding to models I and II are semiconductors,the ones corresponding to model III are semimetals and to model IV metalic.Following the procedure proposed by Mazzoni and Chacham[32],theﬂattening compression is applied in the radial direction by reducing the distance between parallel planes.To quantify the degree of mechanical deformation,theﬂattening ratio(or radial strain)Z is deﬁned asZ¼D02dðÞ=D0ð1Þwhere D0is the original diameter of the non-deformed structure and d is the distance between the twoﬂat planes of the deformed tube cross section.For the investigation of doped(10,0)BNNTs we have analyzed two different situations.Theﬁrst one,labeled as C B,a carbon atom substitutes a boron one creating a B antisite and the second one,a carbon substitutes a nitrogen atom leading to a N antisite which is labeled as C N.Additionally,we have tested the introduction of the substitutional C impurity at two different site locations,ﬁrst at the planar region(labeled as C B-I or C N-I,correspondingly)and on the curved region of the tube(labeled as C B-II or C N-II). Examples of relaxed C B-I and C B-II structures are shown in Fig.1e and f,respectively.As mentioned above,theﬂattening compression is applied in the radial direction by reducing the distance between parallel planes as proposed in Ref.[32].3.Results and discussion3.1.BC2N nanotubesFig.2shows the dependence of the gap energy,E gap,of BC2N models I and II structures as function of theﬂattening ratio.As a general result,it is possible to see that theﬂattening deformation induces a signiﬁcant reduction of E gap,which is a similar to the obtained behavior for CNTs[32].We should mention that,in the speciﬁc case of B–C–N semiconducting materials,comparisons between quasiparticle and DFTﬁrst-principles calculations indi-cate that the local density approximation underestimates the band gap energy by approximately50%[30].Therefore,the present DFT results should be taken in a semiquantitative level, with theﬂattening ratio being underestimated during the transi-tion from semiconductor to metallic electronic behavior.One can see that the energy gap of BC2N model-I nanotubes is always smaller than the obtained values for model-II structures.Such result can be explained by the difference between the numbers of C–C bonds in the structures.In fact,model-I structures have two interlaced chains of C–C and one of B–N bonds,while the model-II have only one chain of such bounds(see Fig.1).In addition,it can be observed for both structure models that for0o Z o0.2thegap Fig.1.Illustration of the BC2N compressed supercells for(a)model-I,(b)model-II, (c)model-III,(d)Model IV,(e)C B-I and(f)C B-II Structures.The black spheres represents the carbon atoms,the small light-gray ones the nitrogen atoms and the gray ones the boron atoms.All the structures were fully relaxed,with residual forces smaller than0.1eV/˚A.S.Azevedo et al./Journal of Solid State Chemistry197(2013)254–260255energy decreases slowly,while for 0.2o Z o 0.5it follows an approximated linear relationship.The decrease of the distance between the two ﬂat planes,which induce the increase of the tube wall curvature,leads to the hybridization of the p orbitals which is more signiﬁcant for large deformations.Therefore,E gap decreases systematically with d (or Z )due to size effects.Concerning structural properties,it could be interesting to point out that the bond lengths in the curved region are usually greater than the corresponding ones in the ﬂat region.Such result is typical for structural deformations and it is similar to the obtained behavior when a monolayer is bent to form a nanotube.The bond lengths in the curved region can increase up to 2%depending on the ﬂattening ratio,bond location and relative orientation to the tube axis.Moreover,it is possible to speculate that the cross section of the relaxed structures followsapproximately a Lame´curve,9x /(D 0þd Z )9n þ9y /d 9n ¼1,where n ranges from 2to 2.4.Fig.3show the calculated band structure of BC 2N model-I and model-II nanotubes for selected ﬂattening ratios.One can see that the electronic states associated to the valence band hardly changes,while the electronic states of the conduction band undergo signiﬁcant modiﬁcations.This result indicates that the reduction of the gap energy is mainly due to changes in the electronic energy levels associated to the conduction bands.Such behavior is similar to the one found for carbon [32]and BN [36]nanotubes.Considering,for example,the nanotube interacting with an AFM tip,it could be interesting to investigate the relation between the compression force and the reduction of E gap .There-fore,in order to obtain the compression force per unit length,F L ,necessary to induce the maximum reduction of the gap energy,i.e.to 0.1eV for model-I and 0.2eV for model-II structures,we apply an approach [32]based on the determination of the strain energy,E strain ,which is deﬁned by E strain ¼E tube ÀE flatð2Þwhere E tube is the calculated total energy of non-deformed tube and E ﬂat is the total energy of the corresponding ﬂattened one.The obtained results are plotted in Fig.4,for both structure models,giving a linear relationship between E strain and 1/d .Taking into account a model where the tube cross section is composed by semicircles and straight lines,as described in [32],E strain can be written as E strain ¼par L =dð3Þwhere a is a constant,r is the surface density of atoms in the ﬂattened tube and L is the length along the tube axis.In spite of the simplicity of such approximation,it is able to reproduce the experimental mechanical response of radial compressed nano-tubes [44].In such approach,the compression force,F ,per unit length,L ,necessary to induce the corresponding reduction of E gap ,is obtained taking the derivative of the strain energy relative to d,Fig.2.Gap energy as a function of the ﬂattening ratio for model-I (solid circles),model-II (upper triangles),model-III (open circles)and model-IV (open squares)BC 2N nanotube structures.The solid and dashed lines are just to guide theeye.Fig.3.Calculated band structures for model-I (left column)and model-II (right column)BC 2N nanotubes as a function of the ﬂattening ratio,Z ,deﬁned by Eq.(1).The Fermi energy level is indicated by the dashed line.S.Azevedo et al./Journal of Solid State Chemistry 197(2013)254–260256givingF L ¼F =L ¼1=L ÀÁð@E strain =@d Þ¼par =d2ð4Þwhere the constant par can be calculated from the slope of the straight lines obtained in Fig.4.Taking into account that thesmaller values of the gap energy takes place at d ¼4˚A,it is found F L ¼7.5N/m for both structure models.Therefore,despite the fact that the present structures have B–N bonds,the obtained value for F L has the same order of magnitude than the one found for CNTs.Fig.5shows the projected density of states (PDOS)associated to B,C,and N atoms for selected values of the ﬂattening ratio of model-I structures.It is possible to see that the major contribu-tion for the electronic states in the energy gap region is associated to the carbon p z orbitals,with small contribution of boron and nitrogen atoms.However,it is not possible to see in the PDOS plots the location of the atoms that contribute to these electronic states,i.e.if such individual atoms are in the curved or in the ﬂattened region.In order to investigate such aspect we calculated the local density of states (LDOS)of the deformed structures.Selected results are shown in Fig.6a and b,which illustrate the electronic density corresponding to the higher occupied molecu-lar orbital (HOMO)and to the lowest unoccupied molecular orbital (LUMO),respectively.For the HOMO state,which corre-sponds to the top of the valence band,the highest electronic densities are localized at the carbon atoms that are bonded to boron.Such C–B pairs are distributed over the whole tube structure and are similar to the localized electronic densities calculated for non-deformed structures (cylindrical tubes).Hence,the HOMO state should not be responsible for the reduction of the gap energy.Therefore,it is possible to infer that such reduction should be attributed to the LUMO state,located at the curved region of the deformed tubes (ﬂattened structures).This electro-nic state is localized at the carbon atoms bonded to nitrogen ones (C–N pairs),with electronic densities which increase with the ﬂattening ratio.This result is consistent with those found for the calculated band structure shown in Fig.3,where the reduction of the gap energy is associated to signiﬁcant modiﬁcations of the energy states at the bottom of the conduction band.Similar results are also obtained for model-II structures (not shown),indicating that the general behavior is basically the same.For model-III and model-IV nanotubes it is obtained the band structures shown in Fig.7for Z ¼0(non compressed)and Z ¼0.5.As mentioned above,uncompressed model-III and IV structures present a metallic behavior,having carbon stripes parallel to the tube axis.Therefore,it is expected that the response of the electronic properties to radial deformations should be quite different from the one obtained for semiconducting model-I and II structures.Indeed,for model-III tubes the radial compression induces the opening of an energy gap of about 0.83eV for Z 40,which remains independent from the ﬂattening ratio,as illu-strated in Fig.2.For model-IV nanotubes the electronic behavior remains unaffected by the radial deformation,presenting a metallic behavior for all values of Z ,as indicated by the band structures shown in Fig.7.Taking into account that the calculated model-III and model-IV nanotubes have an armchair chirality,it is possible to infer that the invariance of E gap with Z can be ascribed to hybridization effect,which is not affected by increasing deformation.Such hypothesis is based on the analogy between the electronic properties of these structures and the ones found for non compressed armchair CNTs that always present a metallic behavior.The gap opening obtained for model-III structurescanFig.4.Calculated strain energy,E strain ,plotted against 1/d ,where d is the distance between the two ﬂat planes of the tube cross section.Circles and triangles indicate obtained values for model-I and model-II structures,respectively.The solid line indicates the obtained linear ﬁtting for model-I structures and the dashed line the corresponding one for model-IInanotubes.Fig.5.Calculated PDOS of selected model-I structures.Straight lines indicate the contribution due to carbon,dotted lines to nitrogen and dashed lines to boron atoms.Model-II structures show similar behavior.The Fermi energy E f level is indicated by the point verticalline.Fig.6.Calculated LDOS of a model-I structure with Z ¼0.5,where:(a )Illustration of the HOMO and (b )LUMO states.The last one,localized in the curved region,is the electronic state responsible for the signiﬁcant reduction of the gap energy.S.Azevedo et al./Journal of Solid State Chemistry 197(2013)254–260257be associated to the larger number of B–N pairs.One can speculate that for the smallest ﬂattening ratio (Z ¼0.05),the structural strain induce the appearance of an energy gap which remains basically unaltered for higher tube curvatures due to the small contribution from the hybridization of p orbitals.3.2.C-doped BN nanotubesThe obtained strain energies for different values of Z ,calcu-lated using Eq.(2),are quoted in Table 1.From such data it is possible to see that smaller stress is obtained when the C impurity is introduced as a substitutional atom in a boron or nitrogen site located at the curved region,which corresponds to C B-II and C N-II structures.It is also possible to observe that E strain increase with Z and depends on the location of the substitutional carbon atom in the nanotube.For the structures where the subtitutional C is located in the curved region,i.e.C B-II and C N-II tubes,the strain energy is smaller when compared with C B-I and C N-I tubes,respectively.Moreover,the strain for C B-II structures reaches the minimum values which are more signiﬁcant as the ﬂattening ratio increases.Therefore,it is possible to conclude that the inclusion of a substitutional C atom reduces the local stress in the curved region producing more stable structures,being C B the antisites that minimize such stress.Moreover,it is interesting to point out that E strain follows a linear relationship when plotted against 1/d .Such result is very similar to the one obtained for BC 2N uncompressed tubes,but with different slope for the obtained straight-line.A summary of the calculated electronic structures for selected nanotubes are illustrated in Fig.8.The band alignment has been done by taking the top of the valence band of non compressed BNNTs as reference.For boron nitride tubes it is obtained a direct band gap where the energies corresponding to the maximum of the valence band and to the minimum of the conduction band are both located at the G point (k ¼0).It is also possible to see,for BNNTs,that the energy states associated to the top of the valence band hardly change,while those associated to the bottom of the conduction band decreases with increasing Z .For the C B-I struc-tures we can see that the carbon impurity introduces an occupiedenergy level in the gap region,close to conduction band.From the calculation results it is possible to observe that the energy of such electronic state does not depends on the tubedeformation.Fig.7.Calculated band structures for model-III (left column)and model-IV (right column)BC 2N nanotubes as a function of the ﬂattening ratio,Z ,deﬁned by Eq.(1).The Fermi energy level is indicated by the dashed line.Table 1Calculated strain energies for C-doped BNNTs as a function of the ﬂattening ratio,Z .It represents the calculated results for substitutional carbon impurities which create a boron (C B )or a nitrogen (C N )antisites,located in the ﬂat (C B-I and C N-I )and curved (C B-II and C N-II )regions.gC B-I C B-II C N-I C N-II 0.050.220.110.200.170.100.730.480.600.540.20 1.49 1.19 1.42 1.240.30 2.25 1.85 2.20 1.960.35 3.36 2.91 3.35 3.130.404.093.574.163.87Fig.8.Calculated band structures for selected BNNTs (ﬁrst line),C B-I (second line)and C N-I (third line)structures.The corresponding ﬂattening ratio is indicated on each column.The Fermi energy level is indicated by the dashed line.S.Azevedo et al./Journal of Solid State Chemistry 197(2013)254–260258However,when Z increases the energy states associated to the conduction band decreases,leading to a signiﬁcant reduction in the gap energy,from 0.7to 0.1eV.A very similar behavior is also found for C B-II structures,where the gap energy decreases with increasing Z ,up to 0.2eV.For C N-I structures the C impurity introduces an empty localized energy level close to the valence band,i.e.a donor state near to the valence band.Consequently,the gap energy is not affected by the radial deformation due to the fact that the energy states associated to the valence band are not changed.Additionally,it is worth to emphasize that the observed changes in E gap ,due to compression,are not associated to the introduction of a substitutional carbon atom.It is in fact asso-ciated to the modiﬁcations of the electronic structure in a similar manner as the one observed for BNNTs.Therefore,the effect of the C doping is limited to the introduction of an impurity level close to the conduction band or to the valence band.Such electronic state is not affected by compression,but induces signiﬁcant changes in the electronic behavior which are independent from the structure deformation.Supposing a doped nanotube under action of an AFM tip and using the same approach as that one described above,it is obtained F L ¼4.9N/m for BNNTs,4.0N/m for C B-I tubes,5.0N/m for C B-II and 4.9N/m for C N-I ones.Therefore,it is possible to conclude that the compression force per unit length is deﬁnitely affected by the impurity location.Further comparison with the obtained F L for CNTs,it is possible to observe a reduction in the range of 29–43%for carbon doped BNNTs.Moreover,Fig.9illustrates the common characteristics of the projected density of states (PDOS)of compressed C-doped BNNTs.Such ﬁgure shows the obtained results for C B-I structures for selected values of Z and represent the general behavior of all calculated struc-tures.From these plots it is possible to see that the states introduced in the gap region are basically associated to carbon and nitrogen atoms.In addition,it is possible infer that such electronic states are affected by the strain associated to the nanotube deformation,where the contribution associated to B atoms decreases with increasing Z .4.ConclusionsIn summary,we investigated the effect of the radial compres-sion on the electronic structure of BC 2N and C-doped BN nano-tubes.It is shown that the electronic properties of BC 2N nanotubes under compression are strongly dependent on the direction of the BN and carbon stripes —i.e.parallel or perpendi-cular to the tube axis.For perpendicular conﬁgurations there are remarkable reductions of the gap energy.The magnitude of the gap reduction with compression is intermediate between those of carbon and boron nitride nanotubes.It is found that the reduction of the energy gap is associated to C–N pairs located at the curved region of the ﬂattened tube.However,when the C stripes are parallel to the tube axis the structures it is found a different behavior.For model-III structures the radial compression induces the opening of an energy gap of about 0.83eV,which is indepen-dent from the ﬂattening ratio.For model-IV nanotubes it is found that the electronic properties remain basically unaffected by the radial deformation,presenting a metallic behavior for all values of Z .Concerning C-doped tubes it is observed that the energy states associated to the conduction band decreases with the ﬂattening ratio,leading to a signiﬁcant reduction in the gap energy.For the special case of C N-I structures the C impurity introduces an empty localized energy level close to the valence band.Therefore,due to the fact that the electronic states associated to the valence band are not affected by the radial deformation,the gap energy is not modiﬁed.Finally,the authors would like to acknowledge the substantial support from the Brazilian agencies:CNPq,FAPEMIG,Capes/Nanobiotec and INCT de Nanomaterias de Carbono.References[1]S.Ijima,Nature (London)354(1991)356.[2]N.Hamada,S.I.Sawada,A.Oshiyama,Phys.Rev.Lett.68(1992)1579.[3]X.Blase,A.Rubio,S.G.Louie,M.L.Cohen,Europhys.Lett.28(1994)335.[4]G.Chopra,R.J.Luyken,K.Cherrey,V.H.Crepi,M.L.Cohen,S.G.Louie,A.Zettl,Science 269(1995)966.[5]A.Rubio,J.Corkill,M.L.Cohen,Phys.Rev.B 49(1994)5081.[6]T.M.Schmidt,R.J.Baierle,P.Piquini, A.Fazzio,Phys.Rev.B bf67(2003)113407.[7]R.Q.Wu,L.Liu,G.W.Peng,Y.P.Feng,Appl.Phys.Lett.86(2005)122510.[12]R.Badzian,T.Niemysky,E.Olkusnik,in:F.A.Glaski (Ed.),Proceedings of theInternational Conference on 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铝合金压铸模英文翻译

program, and then other sections such as biscuit, runner, gate, and overflow were also modeled in the order. Figure 1 shows an example of mold modeling to manufacturer clutch housing parts in application of the high-pressure die casting method. Five gates were used, and the thickness was 3 mm. Figure 2 shows the 3D image of a mold in actual size modeled by using Pro/ENGINEER. The total weight of the mold weighed in 3D modeling was about 12.52 ton, the fixed mold about 3.83 ton, and the moving mold about 8.69 ton, respectively. Two slide cores were operated with five tunnel pins. Specially applied was a chill block with no vacuum device. To prevent dispersion toward the chill block upon casting, a vent insert was added between the moving core and chill block as a shock-observing device to decelerate melting. A slipper was added around the four guide pins to handle problems that might occur to the mold. To prevent the slide core from being pushed toward the hydraulic cylinder upon closing the mold, a retrograding-preventive plate was installed on the fixed mold base. A distributor in contact with the sleeve was designed in a plate type. The hydraulic cylinder applied to

英文翻译

A Facial Aging Simulation Method Using flaccidity deformation criteriaAlexandre Cruz Berg Lutheran University of Brazil.Dept Computer ScienceRua Miguel Tostes, 101. 92420-280 Canoas, RS, Brazil berg@ulbra.tche.br Francisco José Perales LopezUniversitat les Illes Balears.Dept Mathmatics InformaticsCtra Valldemossa, km 7,5E-07071 Palma MallorcaSpainpaco.perales@uib.esManuel GonzálezUniversitat les Illes Balears.Dept Mathmatics InformaticsCtra Valldemossa, km 7,5E-07071 Palma MallorcaSpainmanuel.gonzales@uib.esAbstractDue to the fact that the aging human face encompasses skull bones, facial muscles, and tissues, we render it using the effects of flaccidity through the observation of family groups categorized by sex, race and age. Considering that patterns of aging are consistent, facial ptosis becomes manifest toward the end of the fourth decade. In order to simulate facial aging according to these patterns, we used surfaces with control points so that it was possible to represent the effect of aging through flaccidity. The main use of these surfaces is to simulate flaccidity and aging consequently.1.IntroductionThe synthesis of realistic virtual views remains one of the central research topics in computer graphics. The range of applications encompasses many fields, including: visual interfaces for communications, integrated environments of virtual reality, as well as visual effects commonly used in film production.The ultimate goal of the research on realistic rendering is to display a scene on a screen so that it appears as if the object exists behind the screen. This description, however, is somewhat ambiguous and doesn't provide a quality measure for synthesized images. Certain areas, such as plastic surgery, need this quality evaluation on synthesized faces to make sure how the patient look like and more often how the patient will look like in the future. Instead, in computer graphics and computer vision communities, considerable effort has been put forthto synthesize the virtual view of real or imaginary scenes so that they look like the real scenes.Much work that plastic surgeons put in this fieldis to retard aging process but aging is an inevitable process. Age changes cause major variations in the appearance of human faces [1]. Some aspects of aging are uncontrollable and are based on hereditary factors; others are somewhat controllable, resulting from many social factors including lifestyle, among others [2].1.1.Related WorkMany works about aging human faces have been done. We can list some related work in the simulation of facial skin deformation [3].One approach is based on geometric models, physically based models and biomechanical models using either a particle system or a continuous system.Many geometrical models have been developed, such as parametric model [4] and geometric operators [5]. The finite element method is also employed for more accurate calculation of skin deformation, especially for potential medical applications such as plastic surgery [6]. Overall, those works simulate wrinkles but none of them have used flaccidity as causing creases and aging consequently.In this work is presented this effort in aging virtual human faces, by addressing the synthesis of new facial images of subjects for a given target age.We present a scheme that uses aging function to perform this synthesis thru flaccidity. This scheme enforces perceptually realistic images by preserving the identity of the subject. The main difference between our model and the previous ones is that we simulate increase of fat and muscular mass diminish causing flaccidity as one responsible element for the sprouting of lines and aging human face.In the next section will plan to present the methodology. Also in section 3, we introduce the measurements procedure, defining structural alterations of the face. In section 4, we present a visual facial model. We describe age simulation thrua deformation approach in section 5. In the last section we conclude the main results and future work.2.MethodologyA methodology to model the aging of human face allows us to recover the face aging process. This methodology consists of: 1) defining the variations of certain face regions, where the aging process is perceptible; 2) measuring the variations of those regions for a period of time in a group of people and finally 3) making up a model through the measurements based on personal features.That could be used as a standard to a whole group in order to design aging curves to the facial regions defined.¦njjjpVM2.1Mathematical Background and AnalysisHuman society values beauty and youth. It is well known that the aging process is influenced by several parameters such: feeding, weight, stress level, race, religious factors, genetics, etc. Finding a standard set of characteristics that could possibly emulate and represent the aging process is a difficult proposition.This standard set was obtained through a mathematical analysis of some face measurements in a specific group of people, whose photographs in different ages were available [7]. To each person in the group, there were, at least, four digitized photographs. The oldest of them was taken as a standard to the most recent one. Hence, some face alterations were attained through the passing of time for the same person.The diversity of the generated data has led to the designing of a mathematical model, which enabled the acquiring of a behavior pattern to all persons of the same group, as the form of a curve defined over the domain [0,1] in general, in order to define over any interval [0,Į] for an individual face. The unknown points Įi are found using the blossoming principle [8] to form the control polygon of that face.The first step consisted in the selection of the group to be studied. Proposing the assessment of the face aging characteristics it will be necessary to have a photographic follow-up along time for a group of people, in which their face alterations were measurable.The database used in this work consisted of files of patients who were submitted to plastic surgery at Medical Center Praia do Guaíba, located in Porto Alegre, Brazil.3.MeasurementsAccording to anatomic principles [9] the vectors of aging can be described aswhich alter the position and appearance of key anatomic structures of the face as can be shown in figure 1 which compares a Caucasian mother age 66 (left side) with her Caucasian daughters, ages 37 (right above) and 33 (right below) respectively.Figure 1 - Observation of family groupsTherefore, basic anatomic and surgical principles must be applied when planning rejuvenative facial surgery and treating specific problems concomitantwith the aging process.4.Visual Facial ModelThe fact that human face has an especially irregular format and interior components (bones, muscles and fabrics) to possess a complex structure and deformations of different face characteristics of person to person, becomes the modeling of the face a difficult task. The modeling carried through in the present work was based on the model, where the mesh of polygons corresponds to an elastic mesh, simulating the dermis of the face. The deformations in this mesh, necessary to simulate the aging curves, are obtained through the displacement of the vertexes, considering x(t) as a planar curve, which is located within the (u,v ) unit square. So, we can cover the square with a regular grid of points b i,j =[i/m,j/n]T ; i=0,...,m; j=0,...,n. leading to every point (u,v ) asfrom the linear precision property of Bernstein polynomials. Using comparisons with parents we can distort the grid of b i,j into a grid b'i,j , the point (u,v )will be mapped to a point (u',v') asIn order to construct our 3D mesh we introduce the patch byAs the displacements of the vertexes conform to the certain measures gotten through curves of aging and no type of movement in the face is carried through, the parameters of this modeling had been based on the conformation parameter.4.1Textures mappingIn most cases the result gotten in the modeling of the face becomes a little artificial. Using textures mapping can solve this problem. This technique allows an extraordinary increase in the realism of the shaped images and consists of applying on the shaped object, existing textures of the real images of the object.In this case, to do the mapping of an extracted texture of a real image, it is necessary that the textureaccurately correspond to the model 3D of that is made use [9].The detected feature points are used for automatic texture mapping. The main idea of texture mapping is that we get an image by combining two orthogonal pictures in a proper way and then give correct texture coordinates of every point on a head.To give a proper coordinate on a combined image for every point on a head, we first project an individualized 3D head onto three planes, the front (x, y), the left (y, z) and the right (y, z) planes. With the information of feature lines, which are used for image merging, we decide on which plane a 3D-head point on is projected.The projected points on one of three planes arethen transferred to one of feature points spaces suchas the front and the side in 2D. Then they are transferred to the image space and finally to the combined image space.The result of the texture mapping (figure 2) is excellent when it is desired to simulate some alteration of the face that does not involve a type of expression, as neutral. The picture pose must be the same that the 3D scanned data.¦¦¦ mi nj lk n j m i lk k j i w B v B u B b w v u 000,,)()()(')',','(¦¦ m i nj n jmij i v B u B b v u 00,)()(),(¦¦ m i nj n j m i j i v B u B b v u 00,)()(')','(¦¦¦ mi nj lk n j m i lk k j i w B v B u B b w v u 000,,)()()(')',','(Figure 2 - Image shaped with texturemapping5.Age SimulationThis method involves the deformation of a face starting with control segments that define the edges of the faces, as¦¦¦ mi nj lk n j m i lk k j i w B v B u B b w v u 000,,)()()(')',','(Those segments are defined in the original face and their positions are changed to a target face. From those new positions the new position of each vertex in the face is determined.The definition of edges in the face is a fundamental step, since in that phase the applied aging curves are selected. Hence, the face is divided in influencing regions according to their principal edges and characteristics.Considering the face morphology and the modeling of the face aging developed [10], the face was divided in six basic regions (figure 3).The frontal region (1) is limited by the eyelids and the forehead control lines. The distance between these limits enlarges with forward aging.The orbitary region (2) is one of the most important aging parameters because a great number of wrinkles appears and the palpebral pouch increases [11]. In nasal region (3) is observed an enlargement of its contour.The orolabial region (4) is defined by 2 horizontal control segments bounding the upper and lower lips and other 2 segments that define the nasogenian fold. Figure 3 - Regions considering the agingparametersThe lips become thinner and the nasogenian fold deeper and larger. The mental region (5) have 8 control segments that define the low limit of the face and descend with aging. In ear curve (6) is observed an enlargement of its size. The choice of feature lines was based in the characteristic age points in figure 6.The target face is obtained from the aging curves applied to the source face, i.e., with the new control segment position, each vertex of the new image has its position defined by the corresponding vertex in the target face. This final face corresponds to the face in the new age, which was obtained through the application of the numerical modeling of the frontal face aging.The definition of the straight-line segment will control the aging process, leading to a series of tests until the visual result was adequate to the results obtained from the aging curves. The extremes of the segments are interpolated according to the previously defined curves, obtained by piecewise bilinear interpolation [12].Horizontal and vertical orienting auxiliary lines were defined to characterize the extreme points of the control segments (figure 4). Some points, that delimit the control segments, are marked from the intersection of the auxiliary lines with the contour of the face, eyebrow, superior part of the head and the eyes. Others are directly defined without the use of auxiliary lines, such as: eyelid hollow, eyebrow edges, subnasion, mouth, nasolabial wrinkle andnose sides.Figure 4 - Points of the control segmentsOnce the control segments characterize the target image, the following step of the aging process can be undertaken, corresponding to the transformations of the original points to the new positions in the target image. The transformations applied to the segments are given by the aging curves, presented in section 4.In the present work the target segments are calculated by polynomial interpolations, based on parametric curves [12].5.1Deformation approachThe common goal of deformation models is to regulate deformations of a geometric model by providing smoothness constraints. In our age simulation approach, a mesh-independent deformation model is proposed. First, connected piece-wise 3D parametric volumes are generated automatically from a given face mesh according to facial feature points.These volumes cover most regions of a face that can be deformed. Then, by moving the control pointsof each volume, face mesh is deformed. By using non-parallel volumes [13], irregular 3D manifolds are formed. As a result, smaller number of deformvolumes are necessary and the number of freedom incontrol points are reduced. Moreover, based on facialfeature points, this model is mesh independent,which means that it can be easily adopted to deformany face model.After this mesh is constructed, for each vertex on the mesh, it needs to be determined which particularparametric volume it belongs to and what valueparameters are. Then, moving control points ofparametric volumes in 3D will cause smooth facialdeformations, generating facial aging throughflaccidity, automatically through the use of the agingparameters. This deformation is written in matricesas , where V is the nodal displacements offace mesh, B is the mapping matrix composed ofBernstein polynomials, and E is the displacementvector of parametric volume control nodes.BE V Given a quadrilateral mesh of points m i,j ,, we define acontinuous aged surface via a parametricinterpolation of the discretely sampled similaritiespoints. The aged position is defined via abicubic polynomial interpolation of the form with d m,n chosen to satisfy the known normal and continuity conditions at the sample points x i,j .>@>M N j i ,...,1,...,1),(u @@>@>1,,1,),,( j j v i i u v u x ¦3,,),(n m n m n m v u d v u x An interactive tool is programmed to manipulate control points E to achieve aged expressions making possible to simulate aging through age ranges. Basic aged expression units are orbicularis oculi, cheek, eyebrow, eyelid, region of chin, and neck [14]. In general, for each segment, there is an associated transformation, whose behavior can be observed by curves. The only segments that do not suffer any transformation are the contour of the eyes and the superior side of the head.5.2Deformation approachThe developed program also performs shape transformations according to the created aging curves, not including any quantification over the alterations made in texture and skin and hair color. Firstly, in the input model the subjects are required to perform different ages, as previouslymentioned, the first frame needs to be approximately frontal view and with no expression.Secondly, in the facial model initialization, from the first frame, facial features points are extracted manually. The 3D fitting algorithm [15] is then applied to warp the generic model for the person whose face is used. The warping process and from facial feature points and their norms, parametric volumes are automatically generated.Finally, aging field works to relieve the drifting problem in template matching algorithm, templates from the previous frame and templates from the initial frame are applied in order to combine the aging sequence. Our experiments show that this approach is very effective. Despite interest has been put in presenting a friendly user interface, we have to keep in mind that the software system is research oriented. In this kind of applications an important point is the flexibility to add and remove test facilities. 6.Results The presented results in the following figuresrefer to the emulations made on the frontalphotographs, principal focus of this paper, with theobjective to apply the developed program to otherpersons outside the analyzed group. The comparisonswith other photographs of the tested persons dependon their quality and on the position in which theywere taken. An assessment was made of the new positions, of the control segments. It consisted in: after aging a face, from the first age to the second one, through the use of polynomial interpolation of the control segments in the models in the young age, the new positions are then compared with the ones in the model of a relative of older age (figure 5). The processed faces were qualitatively compared with theperson’s photograph at the same age. Figure 5 - Synthetic young age model,region-marked model and aged modelAlso the eyelid hollow, very subtle falling of the eyebrow, thinning of the lips with the enlarging of the nasion and the superior part of the lip, enlargingof the front and changing in the nasolabial wrinkle.7.ConclusionsModelling biological phenomena is a great deal of work, especially when the biggest part of the information about the subject involves only qualitative data. Thus, this research developed had has a challenge in the designing of a model to represent the face aging from qualitative data.Due to its multi-disciplinary character, the developed methodology to model and emulate the face aging involved the study of several other related fields, such as medicine, computing, statistics and mathematics.The possibilities opened by the presented method and some further research on this field can lead to new proposals of enhancing the current techniques of plastic face surgery. It is possible to suggest the ideal age to perform face lifting. Once the most affected aging regions are known and how this process occurs over time. Also missing persons can be recognized based on old photographs using this technique. AcknowledgementsThe project TIN2004-07926 of Spanish Government have subsidized this work.8. References[1] Burt, D. M. et al., Perc. age in adult Caucasianmale faces, in Proc. R. Soc., 259, pp 137-143,1995.[2] Berg, A C. Aging of Orbicularis Muscle inVirtual Human Faces. IEEE 7th InternationalConference on Information Visualization, London, UK, 2003a.[3] Beier , T., S. Neely, Feature-based imagemetamorphosis, In Computer Graphics (Proc.SIGGRAPH), pp. 35-42, 1992.[4] Parke, F. I. P arametrized Models for FacialAnimation, IEEE Computer & Graphics Applications, Nov. 1982.[5] Waters, K.; A Muscle Model for Animating ThreeDimensional Facial Expression. Proc SIGGRAPH'87,Computer Graphics, Vol. 21, Nº4, United States, 1987. [6] Koch, R.M. et alia.. Simulation Facial SurgeryUsing Finite Element Models, Proceedings of SIGGRAPH'96, Computer Graphics, 1996.[7] Kurihara, Tsuneya; Kiyoshi Arai, ATransformation Method for Modeling and Animation of the Human Face from Photographs, Computer Animatio n, Springer-Verlag Tokyo, pp.45-58, 1991.[8] Kent, J., W. Carlson , R. Parent, ShapeTransformation for Polygon Objects, In Computer Graphics (Proc. SIGGRAPH), pp. 47-54, 1992. [9] Sorensen, P., Morphing Magic, in ComputerGraphics World, January 1992.[10]Pitanguy, I., Quintaes, G. de A., Cavalcanti, M.A., Leite, L. A. de S., Anatomia doEnvelhecimento da Face, in Revista Brasileira deCirurgia, Vol 67, 1977.[11]Pitanguy, I., F. R. Leta, D. Pamplona, H. I.Weber, Defining and measuring ageing parameters, in Applied Mathematics and Computation , 1996.[12]Fisher, J.; Lowther, J.; Ching-Kuang S. Curveand Surface Interpolation and Approximation: Knowledge Unit and Software Tool. ITiCSE’04,Leeds, UK June 28–30, 2004.[13]Lerios, A. et al., Feature-Based VolumeMetamorphosis, in SIGGRAPH 95 - Proceedings,pp 449-456, ACM Press, N.Y, 1995.[14]Berg, A C. Facial Aging in a VirtualEnvironment. Memória de Investigación, UIB, Spain, 2003b.[15]Hall, V., Morphing in 2-D and 3-D, in Dr.Dobb's Journal, July 1993.。

冲压模具-拉深变形特点及分析-浙江职业教育资源网

3
Surrounding Conditions
coefficient of friction.
Temperature, lubrication, and
surface finish.
Factors Affecting Deep Drawing Deformation
Sheet metal thickness
Yield Strength
The lower the strength, the easier the material will deform, but the more likely it will have springback.
Poisson's Ratio
The lower the ratio, the more material elongation will occur during deformation.
Tensile Strength
The higher the strength, the ore likely the material will fracture during deformation.
Young's Modulus
The higher the modulus, the more resistant the material is to deformation.
Application
Kitchen and bathroom fixtures, automotive components, and packaging materials.
Precision
Used for high volume and high precision manufacturing due to its low scrap rate and material efficiency.

infinitesimal deformation theory

infinitesimal deformation theoryInfinitesimal deformation theory is a mathematical concept used in the study of topology and geometry. It deals with the study of infinitesimal changes in the shape or structure of an object, typically a manifold or a space. The goal of this theory is to understand how small perturbations affect the properties of the object being studied.The basic idea behind infinitesimal deformation theory is to consider a smooth family of embeddings or immersions of a manifold into another manifold, where the parameter of the family represents time. As time varies, the manifold undergoes an infinitesimal deformation, which can be described by a vector field along the manifold. This vector field represents the infinitesimal change in the position of each point on the manifold as time progresses.One of the main applications of infinitesimal deformation theory is in the study of moduli spaces, which are spaces that parameterize isomorphism classes of objects with certain properties. For example, the moduli space of Riemann surfaces of genus g parameterizes all compact Riemann surfaces of genus g, up to biholomorphism. Infinitesimal deformation theory allows us to study the local structureof moduli spaces, and in particular, it can be used to show that moduli spaces are smooth and have a natural complex structure.Another important application of infinitesimal deformation theory is in the study of geometric structures on manifolds, such as metrics, connections, and curvature. By considering infinitesimal deformations of these structures, one can study their local behavior and properties, and in particular, one can use this theory to prove existence and uniqueness results for solutions to certain geometric problems.Overall, infinitesimal deformation theory is a powerful tool in the study of topology and geometry, allowing us to understand the behavior of objects under small perturbations and to study the local structure of various moduli spaces and geometric structures.。

Large Deformation Plasticity of Amorphous Solids,

YP (C e,B P ,D P , )D P0
FLOW RULE:
DSebfianec:k2syom (C BeP ,BP)
YP(C e,B P ,D P , )SoSback
S02 sy oC m eT e2 sy o C m e( C C ee ,B P )
Constitutive Equations
h i ( F e , F P , D P , )
Constitutive Theory – Framework
• Frame Indifference
– Euclidean Space
– Amorphous Solids: material are invariant under all rotations of the Relaxed and Reference Configuration
Kinematics – Multiplicative Decomposition of the
Deformation Gradient
FpX
FeX
dxFeXdl Segment of the “current
configuration”
d lFpXdX
Segment of the configuration”
= change in free-volume from initial state
Saturation value:
~ s () s c1 v b (c v)
Micrograph by Roeder et al, 2019
Evolution of the Back Stress: Langevin Statistics undeformed
L0

Deformation meter 英语作文

Deformation meter 英语作文Once by chance, I watched a real documentary in school - Flanglinka "Metamorphosis", I watched after a deep feeling.The documentary focuses on yi Huchen, an urban prince, and Wu Zonghong, an industrious and simple man living in a poor area, exchanging seven days to experience another life. Yi often skips classes and goes to Internet cafes. He only takes part in the show because of the iphone4s. When he got to the mountains, the children welcomed him so warmly that he shed tears for the first time. Here he had to do all the dirty work, feeding the pigs and so on, and in seven days he made friends with every child. Among them he pays special attention to a boy called "small black", yi Huchen helped him to see his father who was imprisoned for making mistakes. In the prison, Xiao Hei and his father hugged each other and cried. Yi Huchen, who was standing beside him, shed tears of excitement again. After returning home, Yi huchen came to the kitchen for the first time and cooked a dinner for his family. He did not mention iphone4S any more. His parents saw him in the eyesand were happy in their hearts.Look at Wu Zonghong, the first time to take a plane, very excited, a new home, to see a lot of novel things: a sofa, a TV and so on a lot of things, dinner, yi father suddenly gave Wu Zonghong one thousand yuan, which is an astronomical figure in his world. Yi's mother and father are kind to him, but he still does what he can. Buy a birthday present for Yi's mother; And sister Yi Rong took photos; In yi mother sick days to take care of her, give her porridge, we all like him, seven days in the past, he returned to the mountains and parents still live a frugal life, he believes that one day will really out of the mountains.Since watching this program, I think we live in a happy family, eat good, with good, but also in the blessing I do not know blessing, sometimes, we like the former yi Huchen, sometimes with parents a few mouth, like this kind of program we want to see more, understand will be more.。

材料科学基础第八章

The combination of a crystallographic plane and, within that plane, a crystallographic direction along which slip (i.e., dislocation motion) occurs.
SLIP SYSTEMS = slip plane+ slip direction
This discrepancy in mechanical strengths could be explained by a type of linear crystalline defect
2020/5/29
Chapter 8 Deformation and Strengthening
4
mechanism
增殖和消亡等现象。至此位错理论得到广泛承认。
2020/5/29
Chapter 8 Deformation and Strengthening
5
mechanism
8-A DEFORMATION MECHANISMS FOR METALS
Dislocation Theory of Crystal Deformation
Chapter 8 Deformation and Strengthening mechanism
第八章 (固体材料的)变形和强化机制
Why Study Deformation and Strengthening Mechanisms?
the nature of dislocations and the role they play in the plastic deformation process

mesh deformation method -回复

mesh deformation method -回复Mesh deformation methodIntroduction:Mesh deformation is a technique used in computer graphics to manipulate the shape of a given mesh. It is widely used in various applications such as character animation, 3D modeling, and virtual reality. In this article, we will discuss the different methods and algorithms used for mesh deformation.1. Linear Blend Skinning (LBS):LBS is the most commonly used method for mesh deformation. It involves associating each vertex of the mesh with a set of bones or joints. These bones/joints are responsible for manipulating the vertices. The deformation of the mesh depends on the transformation of these bones. LBS uses a linear interpolation method to blend the transformations of the associated bones. This technique is efficient and easy to implement, but it may result in some artifacts such as skinning artifacts or undesirable bulging.2. Dual-Quaternion Skinning (DQS):DQS is an extension of LBS that aims to overcome some of its limitations. Instead of using linear interpolation, DQS uses dual quaternions to represent bone transformations. Quaternions provide a compact representation of rotational transformations. Dual quaternions combine a quaternion with a dual part to represent both translation and rotation. This allows for more accurate and smooth deformation of the mesh. DQS is especially useful in preserving volume and preventing bulging artifacts.3. Cage-Based Deformation:Cage-based deformation is a technique that involves associating a control cage or a set of control points with the mesh. The control cage acts as a guide to deform the mesh. The control points are moved, and the mesh deforms accordingly. This method provides more control and precision over the deformation process. It is often used in sculpting applications where artists need to precisely manipulate the shape of the mesh.4. Physics-Based Deformation:Physics-based deformation relies on simulating physical properties such as elasticity, gravity, and collisions to deform the mesh realistically. This method requires solving complex physics equations to calculate the forces acting on the mesh. Implicit methods such as Finite Element Method (FEM) or Implicit Surface Collisions (ISC) are often used for physics-based deformation. This technique is computationally expensive but provides more realistic and dynamic deformations.5. Blendshapes:Blendshapes, also known as morph targets, involve creating a set of predefined target shapes and interpolating between them to deform the mesh. Each target shape represents a specific deformation state, such as a smiling or frowning expression. By blending the weights of these target shapes, the mesh can smoothly transition between different deformations. Blendshapes are widely used in facial animation and can provide highly expressive and natural-looking deformations.Conclusion:Mesh deformation is a fundamental technique in computer graphics that allows for the manipulation of mesh shapes in various applications. Whether through linear blend skinning,dual-quaternion skinning, cage-based deformation, physics-based deformation, or blendshapes, each method has its advantages and limitations. The choice of mesh deformation method depends on the specific application, desired level of control, and the desired realism of the deformations. As technology advances, new methods and algorithms continue to enhance the capabilities and possibilities of mesh deformation in computer graphics.。

制造技术专业英语翻译

7.1 NA TURE OF PLASTIC DEFORMATIONPlastic deformation is the deformation which is permanent and beyond the elastic rang of the material of ten , metals are worked by pfastic deformation because of the beneficial effect that is imparted to the mechanical properties by it. The necessary deformation in a metal can be achieved by application of large amount of mechanical force only or by heating the metal and then applying a small force.7.1 塑性变形本质塑性变形是超过弹性变形范围之后的一种永久变形。

通常，金属采用塑性变形加工是由于可以通过其获得良好的机械性能。

金属所需要的变形可以只通过施加大量的机械力或者通过加热金属并且施加少量的应力来获得。

The deformation of metals, which is caused by the displacement of the atoms is achieved by one or both of the processes called slip and twinning. The details of the microscopic deformation methods can be found in the textbooks of' metallurgy. On the macroscopic scale, when plastic , deformation occurs the metal appears to flow in the solid state along specific directions, which are depedent on the type of processing and the direction of applied force. The crystals or grains of the metal are elongated in the direction of metal flow. This flow of metal can be seen under microscope after polishing and suitable etching of the mental surface . These visible lines are called fibre flow lines, some representative specimens of which are presented in fig金属的变形是由原子排列引起的，这种排列是由被称作滑移和孪生过程中的一种或者两者共同作用导致的。

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1
Introduction
Recent time the strong tendency to inclusion of embedded objects into the scope of theoretical and mathematical physics is observed (see references in [1]). We should relate to the subject all strings and branes models [2, 3], including their supersymmetric and noncommutative generalizations [4], embedding methods of GR [5] and its alternative formulations and generalizations [6], geometrical methods of nonlinear diﬀerential equations theory and jets approach [7] and many other things. Probably, such central position of the ”embedded objects” in modern physics can’t be accidental: it may reﬂect either multidimensional nature of physical reality, observed through all its levels, or some ”immanent” for us, as observers, means for its description. At the same time, majority of the ﬁeld-theoretical models, exploiting embedded objects, reveal amazing and, in our opinion, deep interrelations with some general ideas of elasticity theory of continuous media [8] may be with a number of ”nonstandard” properties such as nonlinearity, plasticity, viscosity, anisotropy, internal spin, nematic or smectic structures or memory [9, 10, 11, 12, 13, 14]. Particularly, in papers [15, 16, 17, 18, 19] it has been shown, that Einstein GR and standard classical solids dynamics admit natural formulation in terms of mechanical straining of thin 4D plates and 4D strings (strongly tensed bars) respectively. Interesting and important problem, arising under such unifying of embedding and elasticity ideas, is to extract and formulate general ideas of continuous media physics in its the most abstract and general form, independent on peculiarities of one or another theory. So, we intend to follow the line of investigations, which can be called general theory of deformational structures (d-structures) with the aim — to formulate and work out universal language for the objects, which are able, in some sense, to be ”deformed”.
∗ sergey@yspu.yar.ru
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Although we’ll restrict ourself by the case of real manifolds, majority of statements will take place after suitable complex generalization, which is necessary for constructing of quantum d-structures. Moreover, some general concepts ”survive” even without smooth structures, but we reserve the more abstract schemes for future. Present paper1 is devoted to some ﬁrst principles of this program. We work out ”deformational terminology” and set some general propositions, statements and relations, which can be recognized within well known theories and which can be used in future works. Within the ﬁrst half of the paper (Sec.2) we consider free d-structures, generalizing kinematics of standard elasticity theory and reﬂecting, mainly, geometrical properties of a number of physical models. The second half (Secc.3,4,5) is devoted to dynamical d-structures, which include, apart from kinematics, some dynamical principle and reﬂect, mainly, physical properties of ﬁeld-theoretical models. Examples of deformational structures, performed in the paper, involve elasticity theory together with its (generally)covariant generalization, Hamiltonian formalism, bundle spaces with invariant connection, thermodynamics, strings and branes theories, classical solids dynamics, gravity, Maxwell electrodynamics. Some more subtle technical questions are investigated in Appendixes. Always, when it is possible we use standard notations of sets theory [21], smooth manifolds theory [22] and (almost2 anywhere) use coordinateless representation of tensor equations. Particularly, we’ll denote by Dom, Im — domains and images of mappings; ρ ∼ — equivalence relation ρ; Dg(A × A) — diagonal of a direct product (i.e. set of pairs (a, a) ∈ A × A); πρ — mapping on quotient space with respect to equivalence ρ; [a]ρ — class of equivalence of the element a with respect to ρ; A ≤ B — A is sub(pseudo)group of (pseudo)group B ; ∂x X = X|x ≡ ∂X/∂x — partial derivative; T (r, s) — space of tensors of covariant valency r and contravariant valency s; ( , ) — scalar product in diﬀerent tensor spaces; , — pairing of tensors and linear functionals over them; Mm×n (C) module of m × n matrices over ring C; Hom(A, B ) — space of linear mappings of modules (linear spaces) A → B.
Abstract Abstract deformational structures, in many aspects generalizing standard elasticity theory, are investigated. Within free deformational structures we deﬁne algebra of deformations, classify them by its special properties, deﬁne motions and conformal motions together with deformational decomposition of manifolds, generalizing isometry of Riemannian spaces and consider some physical examples. In frame of dynamical deformational structures we formulate variational procedure for evolutional and static cases together with boundary conditions, derive dynamical (equilibrium in static case) equations, consider perturbative approach and perform deformational realization of the well known classical ﬁeld-theoretical topics: strings and branes theories, classical mechanics of solids, gravity and Maxwell electrodynamics. PACS: 04.50.+h; 45.40.-f; 46.25.-y; 02.40.Hw ]