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Strain gradient stabilization with dual stress points for the meshfree nodal integration method in inelastic analyses. (English) Zbl 1352.74060
Summary: A nonlinear nodal-integrated meshfree Galerkin formulation based on recently proposed strain gradient stabilization (SGS) method is developed for large deformation analysis of elastoplastic solids. The SGS is derived from a decomposed smoothed displacement field and is introduced to the standard variational formulation through the penalty method for the inelastic analysis. The associated strain gradient matrix is assembled by a B-bar method for the volumetric locking control in elastoplastic materials. Each meshfree node contains two coinciding integration points for the integration of weak form by the direct nodal integration scheme. As a result, a nonlinear stabilized nodal integration method with dual nodal stress points is formulated, which is free from stabilization control parameters and integration cells for meshfree computation. In the context of extreme large deformation analysis, an adaptive anisotropic Lagrangian kernel approach is introduced to the nonlinear SGS formulation. The resultant Lagrangian formulation is constantly updated over a period of time on the new reference configuration to maintain the well-defined displacement gradients as well as strain gradients in the Lagrangian computation. Several numerical benchmarks are studied to demonstrate the effectiveness and accuracy of the proposed method in large deformation inelastic analyses.

MSC:
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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