基于线性互补模型的梯度塑性连续体无网格方法

对梯度塑性连续体提出了一个归结为线性互补问题的数值分析方法. 塑性乘子与位移均为主要未知变量，并采用基于移动最小二乘的无网格方法分别在积分点与节点上插值. 联立弱形式下的平衡方程与积分点上逐点满足的非局部本构方程和屈服准则可以导出一个线性互补问题，并通过Lexico-Lemke算法求解. 构造了一个基于N-R方法的迭代方案，使得不需要形成一致性切线刚度矩阵而仍保持二阶收敛性. 一维和二维的数值算例证明了所提出的方法处理由应变软化引起的应变局部化问题的有效性. 

A MESH-FREE METHOD BASED ON LINEAR COMPLEMENTARY MODEL FOR GRADIENT PLASTICITY CONTINUUM

A numerical method attributed to a solution procedure oflinear complementary problem (LCP) for gradient plasticity continuum isproposed. With the mesh-free method based on moving least-squareapproximation (MLS) procedure, the displacements and plastic multipliertaken as primary field variables are interpolated in terms of theirdiscretized counterparts defined at the nodal points and the integrationpoints, respectively. The weak form of the equilibrium equation along withthe non-local constitutive equation and the non-local yield criterionlocally enforced at each integration point are combined to mathematicallyeduce a normal form of LCP solved by means of Lexico-Lemke algorithm. Aniterative procedure based on the Newton-Raphson method is developed with noneed of consistent tangent elasto-plastic modulus matrix to be derived whilestill retaining the second convergence rate for the solution of the boundaryproblem of gradient plasticity continuum. The numerical results for one andtwo dimensional examples demonstrate the validity of the proposed method indealing with the numerical solution of the strain localization problem dueto strain softening.