Meshfree method for large deformation in dynamic problems

Abstract

We present a new meshless method, Taylor-SPH, for the numerical analysis of large deformation dynamic problems. This method is based on the previous work developed by the authors to solve solid dynamics problems within the framework of small deformation theory. The governing equations are given in terms of stress and velocity using the updated Lagrangian approach. The Jaumann rate of the Cauchy stress is used to get an objective stress rate tensor. The Taylor-SPH method is based on two sets of particles resulting on avoiding the classical tensile instability. In order to assess the accuracy of the proposed method, numerical examples based on elastic material involving large deformation are solved.