A meshfree approach for numerical simulations of large deformation inelastic solids

A meshfree approach for numerical simulations of large deformation inelastic solids is presented. Traditional mesh-based approaches including finite element methods have restrictions that limit their utility. Meshfree methods use approximations constructed entirely in terms of a set of nodal particles that are distributed throughout the domain of interest without the usual restriction of a mesh. Therefore, many of the handicaps associated with the mesh-based finite element methods such as mesh distortion are avoided. Comprehensive study is conducted to demonstrate the feasibility of the meshfree approach in simulating large deformation process, transient dynamic behavior of inelastic solids.; In the 3D meshfree direct simulation of large deformation thin shell structures, a pure displacement-based explicit total Lagrangian formulation is adopted. The relative larger support size of the meshfree shape function may significantly delay the mesh distortion occurrence, thus stretches the computation to a point where the conventional finite element analysis cannot reach without recourse to auxiliary remedies such as re-meshing. Meanwhile, well-posed material model like elasto-plastic and visco-plastic material can be incorporated into the meshfree framework without any simplifications.; One of the most important issues in numerically simulating strain localization phenomena is the mesh-alignment sensitivity. With the introduction of “mesh objectivity” of the meshfree interpolation, the mesh-alignment sensitivity can be alleviated to enhance the robustness of the simulation. Numerical study of dynamically propagating shear band reveals good agreement with experimental observations.; By incorporating wavelets into the meshfree methods, a multi-scale analysis is achieved. Its ease of implementation and capability of detecting high scale solution makes the multi-scale meshfree methods a very attractive candidate in modeling multi-physics processes. A projection algorithm is proposed to degenerate linear dependency between the wavelets and the original meshfree shape functions. The effectiveness of this approach is demonstrated through numerical examples.