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

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.