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An immersed particle modeling technique for the three-dimensional large strain simulation of particulate-reinforced metal-matrix composites. (English) Zbl 1452.74030
Summary: The standard numerical integration of the immersed meshfree Galerkin weak form based on mismatching overlapping integration cells and high-order quadrature rules is very time consuming and requires a large memory in the three-dimensional case. The method even becomes numerically infeasible for the large-scale nonlinear problems in general industrial applications. In this paper, the immersed meshfree Galerkin method is improved with a stabilized particle integration scheme to solve the 3D composite solid problems efficiently. The present immersed particle method introduces a smoothed displacement field to the immersed Galerkin formulation leading to a direct and consistent implementation of a stabilized formulation without the evaluation of the second-order derivatives in the meshfree approximations. Neither numerical viscosity nor artificial control parameters are included in the present formulation for the stabilization. A cube of particulate-reinforced aluminum-matrix composite under large strain is analyzed using an explicit time integration scheme to demonstrate the accuracy and the applicability of the proposed modeling technique to the three-dimensional nonlinear simulation of composite solids.
##### MSC:
 74E30 Composite and mixture properties 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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