应变梯度理论及其数值方法研究进展  

Research progress on the strain gradient theories and related numerical methods

作　　者：李雷[1,2] 周毅英[1] 李文杰[3] 谢水生[2] 

机构地区：[1]河南理工大学土木工程学院,河南焦作454003 [2]北京有色金属研究总院有色金属材料制备加工国家重点实验室,北京100088 [3]河南信息工程学校,河南郑州450011

出　　处：《河南理工大学学报（自然科学版）》2009年第1期113-118,131,共7页Journal of Henan Polytechnic University（Natural Science）

基　　金：国家“十一五”科技支撑计划项目(2007BAE23B04);河南理工大学青年骨干教师基金资助项目(649027)

摘　　要：介绍了微尺度下材料变形过程中的尺度效应以及应变梯度理论的发展历史;主要介绍了Toupin-Mindlin应变梯度弹性理论和Fleck-Hutchinson应变梯度塑性理论,包括偶应力理论和拉伸与旋转梯度理论;阐述了应变梯度理论在解释尺度效应方面的成功应用及应变梯度理论的数值实施方法的发展现状;指出了应变梯度理论及其数值方法目前面临的困难以及发展方向.Size effects phenomena emerged in the deformation processes under the micro -scale are introduced, as well as developing history and applications of strain gradient theory. Especially, the Toupin - Mindlin strain gradient elasticity and the Fleck - Hutchinson strain gradient plasticity, which including the couple stress theory, the stretch and the rotation theory, are emphasized. Furthermore, the successful applications of the strain gradient theories in the explaining the size effects are expatiated. Present status and future development of the numerical implementation approaches on the strain gradient theories are reviewed. Finally, the difficulties and the development directions of the strain gradient theories and their numerical implementation methods are pointed out.

关 键 词：尺度效应 应变梯度理论 偶应力 材料内禀特征长度 有限单元法 

分 类 号：O343[理学—固体力学] O344[理学—力学]