A convected particle least square interpolation material point method

Abstract

Summary Applying the convected particle domain interpolation (CPDI) to the material point method has many advantages over the original material point method, including significantly improved accuracy. However, in the large deformation regime, the CPDI still may not retain the expected convergence rate. The paper proposes an enhanced CPDI formulation based on least square reconstruction technique. The convected particle least square interpolation (CPLS) material point method assumes the velocity field inside the material point domain as nonconstant. This velocity field in the material point domain is mapped to the background grid nodes with a moving least squares reconstruction. In this paper, we apply the improved moving least squares method to avoid the instability of the conventional moving least squares method due to a singular matrix. The proposed algorithm can improve convergence rate, as illustrated by numerical examples using the method of manufactured solutions.

Toward a local maximum‐entropy material point method at finite strain within a B‐free approach

“…This statement can be extended to the LME approximants case according to further research. 4,6,54 In the subsequent years, an increasing number of publications is this direction [55][56][57] shows that the issue of numerical integration is still an active trend of research among the meshfree community.…”

“…This statement can be extended to the LME approximants case according to further research. 4,6,54 In the subsequent years, an increasing number of publications is this direction [55][56][57] shows that the issue of numerical integration is still an active trend of research among the meshfree community. Other source of energy dissipation is the current time integration scheme since the same benchmark performed by the energy-momentum conserving algorithm employed by Sulsky and Love 12 does not exhibits numerical damping.…”

Modelling of shear zones during quasi-static granular silo flow using material point method (MPM)

“…MPM is still in development with no formal proof of convergence available. The method is being constantly improved with recent developments showing a consistent rate of convergence [72] and strategies to deal with identified errors. An overview of some of the method errors is given below.…”

An implicit locking‐free B‐spline Material Point Method for large strain geotechnical modelling

“…Apart from utilising the higher-order shape function, the Moving Least Squares (MLS) shape function is also usually used to mitigate the cell crossing noise. [16][17][18] In the current literature, the MLS shape function has only been used in the explicit MPM solver, and the implicit MLS-MPM still needs to be studied.…”