A Discontinuous Galerkin Material Point Method for the simulation of impact problems in solid mechanics

Adrien Renaud (1) , Thomas Heuzé (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique

The material point method is extended in this work to the Discontinuous Galerkin approximation framework for the simulation of impacts on elastic and hyperelastic solids. The formulation is based on the weak form of conservation laws on each cell of an eulerian grid in which volume integrals are discretized on a set of material points lying in that cell, and on the computation of Godunov fluxes at cells faces. The resulting method is first derived within the small strains framework and illustrated on a one-dimensional and a two-dimensional problem of impact on an elastic media. Then a one-dimensional hyperelastic problem of a solid undergoing large strains is presented, and a comparison is performed with an analytical solution.

Mots clés: Material Point Method; Discontinuous Galerkin; dynamic impact; elastic solid; hyperelastic solid

Domaines: Mécanique des structures [physics.class-ph]

Adrien Renaud, Thomas Heuzé. A Discontinuous Galerkin Material Point Method for the simulation of impact problems in solid mechanics. 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2017), Jun 2017, Rhodes Island, Greece. ⟨10.7712/120117.5678.17188⟩. ⟨hal-01913197⟩