Conforming local meshfree method

Abstract

SUMMARYThis work is motivated by the current numerical limitation in multiscale simulation of ductile fracture processes at scale down to the microstructure size and aims to overcome the difficulties in 3D complicated mesh generation and locally extremely large strain analysis (local mesh distortion). The proposed 'conforming local meshfree approximation' directly and exactly satisfies displacement compatibility on a non-conforming assembly mesh. Local meshfree nodes, which can be freely placed and move on a finite element mesh, describe local large deformation. The improved accuracy on non-conforming mesh, the exactness in geometry representation on a structured mesh, and the good tolerance to mesh distortion are demonstrated by numerical examples.

Large-Scale Simulation of Ductile Fracture Process of Microstructured Materials

“…1) We employ the multiresolution continuum theory. [21][22][23][24][25][26][27][28][29] In the following formulation,   , D σ describes the stress in the matrix material including the secondary particles.…”

A Large Strains Finite Element Multiscale Approach

“…However, they are using either a different numerical method, i.e not FEM, or they are performing the technique with a distinct strategy to the one presented here. Inside the first group, the work by [31] deals with large strains within a multiscale meshfree method framework. In the second group, i.e.…”