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The Material Point Method (MPM) represents an alternative simulation technique as to, e.g., the Finite-Element-Method. Within the MPM, physical bodies are discretized as material points in a Lagrangian sense where all kinematic and constitutive quantities are stored on. The actual numerical solution of the balance equations is solved on the nodes of the Eulerian background grid, see [1], where it is common practice to use the same fixed grid geometry throughout the whole simulation. As the material points move independently of the background grid, mesh distortion as in, e.g., FEM simulations is completely avoided. In this contribution, numerical examples of dynamic processes subject to large deformations are analyzed and evaluated. These examples show an influence of the grid position in mechanical quantities like stresses. As the focus of this contribution is on the improvement of numerical results, a technique at almost no computational cost is presented. Within this technique, the origin of the background grid is shifted randomly for a small distance in each direction at the beginning of each time step. As a result, mesh-influences in stresses are averted as the grid translations can be interpreted as smearing the grid over time.
References
[1] D. Sulsky, Z. Chen und H. Schreyer. “A particle method for history-dependent materials”. In: Computer Methods in Applied Mechanics and Engineering. 118.1-2 (1994), S. 179–196. doi: 10.1016/0045-7825(94)90112-0.
