Stochastic Material Point Method for Analysis in Non-Linear Dynamics of Metals

A stochastic material point method is proposed for stochastic analysis in non-linear dynamics of metals with varying random material properties. The basic random variables are parameters of equation of state and those of constitutive equation. In conjunction with the material point method, the Taylor series expansion is employed to predict first- and second-moment characteristics of structural response. Unlike the traditional grid methods, the stochastic material point method does not require structured mesh; instead, only a scattered cluster of nodes is required in the computational domain. In addition, there is no need for fixed connectivity between nodes. Hence, the stochastic material point method is more suitable than the stochastic method based on grids, when solving dynamics problems of metals involving large deformations and strong nonlinearity. Numerical examples show good agreement between the results of the stochastic material point method and Monte Carlo simulation. This study examines the accuracy and convergence of the stochastic material point method. The stochastic material point method offers a new option when solving stochastic dynamics problems of metals involving large deformation and strong nonlinearity, since the method is convenient and efficient.