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,810 北京科技大学学报 第29卷 参考文献 cation predictions.Int J Solids Struct.2001.38.833 [8]Gao HJ.Huang Y G.Taylor-based nonlocal theory of plasticity. [1]Aifantis EC.On the role of gradients in the localization of defor- mation and fracture.Int J Eng Sci.1992.30:1279 Int J Solids Struct.2001.38:2615 [2]Aifantis EC.Strain gradient interpretation of size effects.Int J [9]Simo JC.Rifa MS.A class of mixed assumed strain methods and Fract,1999,95:299 the method of incompatible modes.Int J Numer Methods Eng. 1990,29:1595 [3]Fleck N A,Hutchinson J W.A phenomenological theory for strain gradient effects in plasticity.J Mech Phys Solids.1993. [10]陈章华，刘洪波，马文江·增强假设变形梯度有限元方法稳定 41,837 性计算.北京科技大学学报，2005,27(5)：556 [4]Fleck N A,Hutchinson J W.Strain gradient plasticity.Adv Appl [11]Glaser S,Armero F.On the formulation of enhanced strain fi- Mch,1997,33:295 nite elements in finite deformations.Eng Comput,1997,14; 759 [5]Fleck N A.Muller G M.Ashby M F,et al.Strain gradient plas- ticity:theory and experiment.Acta Metall Master,1994.42: [12]Chen Z H.Lee T C.Tang C Y.Numerical simulation of a sheet 475 metal extrusion process by using thermal-mechanical coupling [6]Bassani JL.Incompatibility and a simple gradient theory of plas EAS FEM.J Univ Sci Technol Beijing.2002.19:378 ticity.J Mech Phys Solids.2001,49:1983 [13]Florando J N.Nix W D.A microbeam bending method for [7]Bassani JL.Needleman A.van der Giessen E.Plastic flow in a studying stress"strain relations for metal thin films on silicon for substrates.J Mech Phys Solids.2005,53.619 composite:a comparison of nonlocal continuum and discrete dislo- Assumed strain finite element method based on the theory of strain gradient CHEN Zhanghua,YU Shunli Applied Science School,University of Science and Technology Beijing Beijing 100083.China ABSTRACI An assumed strain finite element method based on the theory of strain gradient was proposed to explore the size effect that frequently exhibited in micro-beam bending.In element design,strain gradient terms were obtained by using numerical integration of a cell constructing around a Gaussian point.An equivalent strain gradient term was incorporated into the constitutive model to reflect the effect of highly localized inhomogeneous deformation.In this way,an assumed strain finite element method program was developed.To validate the per- formance of the proposed method,a numerical simulation of micro-beam bending was carried out.Numerical re- sults show a good agreement with the reported experimental data.It is concluded that the proposed approach is of good capability to reflect the response of microstructure. KEY WORDS assumed strain finite element method;strain gradient;scale effect;micro-beam参 考 文 献 ［1］ Aifantis E C．On the role of gradients in the localization of deformation and fracture．Int J Eng Sci199230：1279 ［2］ Aifantis E C．Strain gradient interpretation of size effects．Int J Fract199995：299 ［3］ Fleck N AHutchinson J W．A phenomenological theory for strain gradient effects in plasticity．J Mech Phys Solids1993 41：837 ［4］ Fleck N AHutchinson J W．Strain gradient plasticity．Adv Appl Mech199733：295 ［5］ Fleck N AMuller G MAshby M Fet al．Strain gradient plasticity：theory and experiment．Acta Metall Master199442： 475 ［6］ Bassani J L．Incompatibility and a simple gradient theory of plasticity．J Mech Phys Solids200149：1983 ［7］ Bassani J LNeedleman Avan der Giessen E．Plastic flow in a composite：a comparison of nonlocal continuum and discrete dislocation predictions．Int J Solids Struct200138：833 ［8］ Gao H JHuang Y G．Taylor-based nonlocal theory of plasticity． Int J Solids Struct200138：2615 ［9］ Simo J CRifa M S．A class of mixed assumed strain methods and the method of incompatible modes．Int J Numer Methods Eng 199029：1595 ［10］ 陈章华刘洪波马文江．增强假设变形梯度有限元方法稳定 性计算．北京科技大学学报200527（5）：556 ［11］ Glaser SArmero F．On the formulation of enhanced strain finite elements in finite deformations．Eng Comput199714： 759 ［12］ Chen Z HLee T CTang C Y．Numerical simulation of a sheet metal extrusion process by using therma-l mechanical coupling EAS FEM．J Univ Sci Technol Beijing200219：378 ［13］ Florando J NNix W D．A microbeam bending method for studying stress-strain relations for metal thin films on silicon for substrates．J Mech Phys Solids200553：619 Assumed strain finite element method based on the theory of strain gradient CHEN ZhanghuaY U Shunli Applied Science SchoolUniversity of Science and Technology BeijingBeijing100083China ABSTRACT An assumed strain finite element method based on the theory of strain gradient was proposed to explore the size effect that frequently exhibited in micro-beam bending．In element designstrain gradient terms were obtained by using numerical integration of a cell constructing around a Gaussian point．An equivalent strain gradient term was incorporated into the constitutive model to reflect the effect of highly localized inhomogeneous deformation．In this wayan assumed strain finite element method program was developed．To validate the performance of the proposed methoda numerical simulation of micro-beam bending was carried out．Numerical results show a good agreement with the reported experimental data．It is concluded that the proposed approach is of good capability to reflect the response of microstructure． KEY WORDS assumed strain finite element method；strain gradient；scale effect；micro-beam ·810· 北 京 科 技 大 学 学 报 第29卷