A generalized finite element method without extra degrees of freedom for large deformation analysis of three-dimensional elastic and elastoplastic solids

The generalized finite element method (GFEM) is versatile and powerful in the numerical analysis of various engineering problems. However, its application to large deformation analysis of elastoplastic solids is rare, especially in three dimensions (3D), since it suffers from singular system matrix and awkward implementation. This issue is caused by the extra degrees of freedom (DOFs) of GFEM. In this work, a nonlinear GFEM for large deformation analysis of elastic and elastoplastic solids in 3D is developed by using the extra-DOF-free enrichments proposed by Tian (2013) Updated Lagrangian (UL) formulation incorporating both geometric and material nonlinearities is employed and hyperelastic and hypoelastic-plastic constitutive models are considered. As a result of the elimination of the extra DOFs, implementation of the developed method is much more convenient than the standard GFEM and singular system matrix does not present. The capability of the proposed nonlinear GFEM in modeling three-dimensional large elastoplastic deformations is investigated by several typical examples. Numerical results demonstrate that, in comparison to the traditional finite element method, the proposed nonlinear GFEM is remarkably more accurate and stable. Particularly, in analysis of extreme deformations, the commercial software ABAQUS fails even when sophisticated elements are used, however the proposed nonlinear extra-DOF-free GFEM is still stable and converged results can be obtained.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper presents a nonlinear generalized finite element method (GFEM) for large deformation analysis of elastic and elastoplastic solids in three dimensions. By eliminating the extra degrees of freedom, the developed method is more convenient to implement than the standard GFEM and does not suffer from singular system matrix. Numerical results demonstrate that the proposed nonlinear GFEM is remarkably more accurate and stable than the traditional finite element method in modeling three-dimensional large elastoplastic deformations.