# Meshless method for modeling large deformation with elastoplasticity

## K-REx Repository

 dc.contributor.author Ma, Jianfeng dc.date.accessioned 2007-10-05T14:19:49Z dc.date.available 2007-10-05T14:19:49Z dc.date.issued 2007-10-05T14:19:49Z dc.identifier.uri http://hdl.handle.net/2097/402 dc.description.abstract Over the past two decades meshless methods have attracted much attention owing to their advantages in adaptivity, higher degree of solution field continuity, and capability to handle moving boundary and changing geometry. In this work, a meshless integral method based on the regularized boundary integral equation has been developed and applied to two-dimensional linear elasticity and elastoplasticity with small or large deformation. en 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. dc.language.iso en_US en dc.publisher Kansas State University en dc.subject Meshless method en dc.subject Large deformation en dc.subject Elastoplasticity en dc.subject Subtraction method en dc.subject Singularity removal en dc.subject Local boundary integral equation en dc.title Meshless method for modeling large deformation with elastoplasticity en dc.type Dissertation en dc.description.degree Doctor of Philosophy en dc.description.level Doctoral en dc.description.department Department of Mechanical and Nuclear Engineering en dc.description.advisor Prakash Krishnaswami en dc.description.advisor Xiao J. Xin en dc.subject.umi Engineering, Mechanical (0548) en dc.date.published 2007 en dc.date.graduationmonth December en
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