Abstract
The B-spline material point method (BSMPM) has proved to be a promising numerical method for modeling problems with large deformations. While the cell-crossing noise is alleviated by using high-order continuous B-spline basis functions, the BSMPM still suffers from reduced accuracy arising from quadrature errors when simulating large-deformation problems. In this work, a quadrature scheme for the information mapping and the internal force calculations in the BSMPM is developed to substitute for the widely adopted numerical integration at the material particles or the Gauss points within the particle domain. Representative numerical examples of elastic and elasto-plastic large-deformation problems demonstrate the highly enhanced accuracy and convergence of the BSMPM simulations for solid mechanics problems involving large deformations by the proposed quadrature scheme. Moreover, it is shown that, compared to the algorithm of applying numerical Gauss quadrature in the particle domain, the proposed integration scheme is a more favorable option for improving the capability and efficiency of the BSMPM in the analysis of large-deformation problems.
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