摘要
从一般的偶应力理论出发,基于Hellinger-Reissner变分原理,通过对有限元离散体系的位移试解引入非协调位移函数,得到了偶应力理论下有限元离散系统的能量相容条件,并由此建立了应变梯度杂交元的应力函数优化条件.根据该优化条件,构造了一个C0类的平面4节点梯度杂交元,数值结果表明,该单元对可压缩和不可压缩状态的梯度材料均可给出合理的数值结果,再现材料的尺度效应.
Recent experiments have shown that materials will display strong scale effect when the scale of non-uniform plastic deformation field associated their intrinsic length scale is on the order of microns. In order to explain such scale effect phenomena, Fleck and Hutchinson developed a couple stress theory of strain gradient plasticity based on the reduced couple stress theory, which incorporates the rotation gradient of deformation into constitutive model, and introduces a material characteristic length parameter related to the rotation gradient. Theoretical predictions agree well with the micro-torsion and micro-bending experiments. In the finite element implementation of Fleck-Hutchinson couple stress plasticity, the higher order nature of theory requires that both the displacement and its first-order derivatives to be continuous across the adjacent elements' boundaries. Noticed that the micro-rotation *********, an independent kinematic quantity with no direct dependence on displacement u, is introduced in the general couple stress theory. This enables the C0-continuous element to be developed based on the general couple stress theory. Fitting within the framework of general couple stress theory, the energy consistency condition of the discrete finite element system for couple stress strain gradient theory is derived by introduction of incompatible displacement trial functions. Furthermore, the optimization condition of stress trial functions for hybrid element of strain gradient theory is constructed based the energy consistency condition. A 4-node C0 kind hybrid element is designed in terms of the optimization condition. Numerical tests show that the scale effects can be reflected with the element designed in the paper and reliable results is delivered both for compressible and incompressible materials.
出处
《力学学报》
EI
CSCD
北大核心
2005年第3期301-306,共6页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(10172078
50374014)
