摘要
对梯度塑性连续体提出了一个有限元方法．内状态变量的Ｌａｐｌａｃｉａｎ的确定基于它在求积点邻域的最小二乘方多项式近似．具体地考虑了具有一点求积和Ｈｏｕｒｇｌａｓｓ控制特点的基于胡海昌－Ｗａｓｈｉｚｕ变分原理的混合应变元和单元平均意义下的ｖｏｎ－Ｍｉｓｅｓ屈服准则．解析地导出了梯度塑性下一致性单元切线刚度矩阵和速率本构方程的一致性积分算法．在所建议的非局部化途径中求积点的一致性条件在非局部化意义下逐点精确满足．
A finite element method for gradient plastic continuum is presented The Laplacian of the internal state variable is determined on the basis of a least square polynomial approximation of the internal state variable around each integration point A mixed strain element with one point guadrature and hourglass control derived from the Hu-Washizu principle and the average von Mises yield criterion are particularly considered The consistent element stiffness matrix and consistent algorithm for the integration of the rate constitutive equation for the gradient plasticity are analytically derived The consistency condition is exactly satisfied at each integration point in the non local sense in the proposed approach The numerical examples illustrate the capability and performance of the present finite element method for the non classical continuum in solving for the strain localization problems
出处
《力学学报》
EI
CSCD
北大核心
1996年第5期575-584,共10页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金
教委博士点基金
关键词
梯度塑性
应变局部化
有限元
塑性连续性
gradient plasticity, strain localization, finite element, consistent algorithm
