Updated Lagrangian Taylor-SPH method for elastic dynamic problems

This paper presents a discussion on the properties of the collocation meshfree method, the Updated Lagrangian Taylor-SPH (UL-TSPH), for dynamic problems in solid mechanics. The PDEs are written in mixed form in terms of stress and velocity for the elastodynamics problems. Two sets of particles are used to discretize the partial differential equations, resulting on avoiding the tensile instability inherent to classical SPH formulations. Numerical examples ranging from propagation of a shock wave in an elastic bar to a stationary Mode-I semi-Infinite cracked plate subjected to uniaxial tension are used to assess the performance of the proposed method