2D Finite Volume Lagrangian Scheme in Hyperelasticity and Finite Plasticity

Abstract

System of conservation laws develop discontinous solutions, which can be captured by conservative and consistent Finite Volume schemes. In Lagrangian schemes, the mesh is moving; therefore material interfaces are well simulated. Cell-centered Lagrangian Finite Volume schemes have been recently developed in compressible hydrodynamic [J. Comput. Phys. 228:5160–5183, 2009, Comptes Rendus Academie des Sciences 331:327–372, 2003, Siam J. Sci. Comp. 29, 2007]. This paper shows how to extend these schemes to material strength. Moreover, we show that with an appropriate equation of state, this extension allows to simulate some plastic phenomenons.