A dynamic adaptation technique for the material point method

The Lagrangian Material Point Method (MPM) [1, 2] has been implemented into the Eulerian shock physics code CTH[3], at Sandia National Laboratories. Since the MPM uses a background grid to calculate gradients, the method can numerically fracture if an insufficient number of particles per cell are used in high strain problems. Numerical fracture happens when the particles become separated by more than a grid cell leading to a loss of communication between them. One solution to this problem is the Convected Particle Domain Interpolation (CPDI) technique[4] where the shape functions are allowed to stretch smoothly across multiple grid cells, which alleviates this issue but introduces difficulties for parallelization because the particle domains can become non-local. This paper presents an approach where the particles are dynamically split when the volumetric strain for a particle becomes greater than a set limit so that the particle domain is always local, and presents an application to a large strain problem