Stress Wave Propagation Using Mesh-Free Material Point Method

Numerical simulation has become prominent in virtually all fields of engineering. It not only helps solve complicated problems but also gives a lot of information at a low cost and in a short amount of time, mainly when experimental visualization is complex. Most mechanical simulations incorporate the finite element method (FEM), where the domain is divided into elements. Although the technique is well developed and widely used, it reaches its limits when elements get distorted in large deformation problems and lead to premature simulation termination. In large distortion problems, elements are deleted, leading to errors. This problem is not observed with mesh-less or mesh-free methods in which the material domain is discretized into a material point (MP) or particles. Among the already developed mesh-less methods, MPM has become significantly popular among researchers as it captures the physical phenomenon in a better way. This paper observes stress wave propagation using standard MPM with C0 basis functions in a steel bar. The MPM code was developed using Julia programming language. Stress waves at different axial positions were compared quantitively with FEM results from Abaqus, which follow the same trend as stated in the literature.