Meshfree method for large deformation in dynamic problems

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

Updated Lagrangian Taylor-SPH method for large deformation in dynamic problems

In this paper, the updated Lagrangian Taylor-SPH meshfree method is applied to the numerical analysis of large deformation and failure problems under dynamic conditions. The Taylor-SPH method is a meshfree collocation method developed by the authors over the past years. The governing equations, a set of first-order hyperbolic partial differential equations, are written in mixed form in terms of stress and velocity. This set of equations is first discretized in time by means of a Taylor series expansion in two steps and afterwards in space using a corrected form of the SPH method. Two sets of particles are used for the computation resulting on the elimination of the classical tensile instability. In the paper presented herein the authors propose an updated Lagrangian Taylor-SPH approach to address the large deformations of the solid, and therefore the continuous re-positioning of the particles. In order to illustrate the performance and efficiency of the proposed method, some numerical examples based on elastic and viscoplastic materials involving large deformations under dynamic conditions are solved using the proposed algorithm. Results clearly show that the updated Lagrangian Taylor-SPH method is an accurate tool to model large deformation and failure problems under dynamic loadings. © 2019With funding from the Spanish government through the "María de Maeztu Unit of Excellence" accreditation (MDM-2017-0737