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中文摘要：
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。
英文摘要：
A numerical method attributed to a solution procedure of linear complementary problem （LCP） for gradient plasticity continuum is proposed. With the mesh-free method based on moving least-square approximation （MLS） procedure, the displacements and plastic multiplier taken as primary field variables are interpolated in terms of their discretized counterparts defined at the nodal points and the integration points, respectively. The weak form of the equilibrium equation along with the non-local constitutive equation and the non-local yield criterion locally enforced at each integration point are combined to mathematically educe a normal form of LCP solved by means of Lexico-Lemke algorithm. An iterative procedure based on the Newton-Raphson method is developed with no need of consistent tangent elasto-plastic modulus matrix to be derived while still retaining the second convergence rate for the solution of the boundary problem of gradient plasticity continuum. The numerical results for one and two dimensional examples demonstrate the validity of the proposed method in dealing with the numerical solution of the strain localization problem due to strain softening.
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