Stochastic meshfree method for elasto-plastic damage analysis

This paper presents a stochastic meshfree method for solving boundary-value problems in damage mechanics under elasto-plastic conditions. Isotropic ductile damage evolution law is used to model the coupled elasto-plastic damage growth. Uncertainty associated with initial damage in materials is considered as random field. Moving least squares shape function method and Karhunen Loève expansion method are used for random field discretization. Statistical parameters of the response quantities are computed using perturbation method. The proposed method involves a new stochastic stress update procedure to solve the nonlinear equations in terms of discretized random variables arising from perturbation of equilibrium equations system. Numerical examples comprising of one and two dimensional problems are presented to illustrate the effectiveness of proposed method.