Simplified second-order Godunov-type methods
SIAM Journal on Scientific and Statistical Computing
A high-order Eulerian Godunov method for elastic-plastic flow in solids
Journal of Computational Physics
Computer Simulation of Dynamic Phenomena
Computer Simulation of Dynamic Phenomena
A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Solid-fluid diffuse interface model in cases of extreme deformations
Journal of Computational Physics
Discretization of hyperelasticity on unstructured mesh with a cell-centered Lagrangian scheme
Journal of Computational Physics
Journal of Computational Physics
Eulerian adaptive finite-difference method for high-velocity impact and penetration problems
Journal of Computational Physics
An Eulerian algorithm for coupled simulations of elastoplastic-solids and condensed-phase explosives
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.49 |
An Eulerian conservative hyperbolic model of isotropic elastic materials subjected to finite deformation is addressed. It was developed by Godunov [S.K. Godunov, Elements of continuum mechanics, Nauka, Moscow, 1978 (in Russian) and G.H. Miller, P. Colella, A high-order Eulerian Godunov method for elastic-plastic flow in solids, J. Comput. Phys. 167 (2001) 131-176]. Some modifications are made concerning a more suitable form of governing equations. They form a set of evolution equations for a local cobasis which is naturally related to the Almansi deformation tensor. Another novelty is that the equation of state is given in terms of invariants of the Almansi tensor in a form which separates hydrodynamic and shear effects. This model is compared with another hyperbolic non-conservative model which is widely used in engineering sciences. For this model we develop a Riemann solver and determine some reference solutions which are compared with the conservative model. The numerical results for different tests show good agreement of both models for waves of very small and very large amplitude. However, for waves of intermediate amplitude important discrepancies between results are clearly visible.