Meshless method for modeling large deformation with elastoplasticity
The development of the meshless integral method and its application to two-dimensional linear elasticity is described first. The governing integral equation is obtained from the weak form of elasticity over a local sub-domain, and the moving least-squares approximation is employed for meshless function approximation. This formulation incorporates: a subtraction method for singularity removal in the boundary integral equation, a special numerical integration for the calculation of integrals with weak singularity which further improves accuracy, a collocation method for the imposition of essential boundary conditions, and a method for incorporation of natural boundary conditions in the system governing equation. Next, elastoplastic material behavior with small deformation is introduced into the meshless integral method. The constitutive law is rate-independent flow theory based on von Mises yielding criterion with isotropic hardening. The method is then extended to large deformation plasticity based on Green-Naghdi’s theory using updated Lagrangian description. The Green-Lagrange strain is decomposed into the elastic and plastic part, and the elastoplastic constitutive law is employed that relates the Green-Lagrange strain to the second Piola-Kirchhoff stress. Finally, a pre- and post-processor for the meshless method using node- and pixel-based approach is presented. Numerical results from the meshless integral method agree well with available analytical solutions or finite element results, and the comparisons demonstrate that the meshless integral method is accurate and robust. This research lays the foundation for modeling and simulation of metal cutting processes.
School:Kansas State University
School Location:USA - Kansas
Source Type:Master's Thesis
Keywords:meshless method large deformation elastoplasticity subtraction singularity removal local boundary integral equation engineering mechanical 0548
Date of Publication:01/01/2007