A conservative Eulerian formulation of the equations for elastic flow
Advances in Applied Mathematics
Vorticity errors in multidimensional Lagrangian codes
Journal of Computational Physics
Computational methods in Lagrangian and Eulerian hydrocodes
Computer Methods in Applied Mechanics and Engineering
Formulations of artificial viscosity for multi-dimensional shock wave computations
Journal of Computational Physics
The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
Journal of Computational Physics
A free-Lagrange augmented Godunov method for the simulation of elastic-plastic solids
Journal of Computational Physics
A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing
Journal of Computational Physics
Journal of Computational Physics
A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems
SIAM Journal on Scientific Computing
Modelling wave dynamics of compressible elastic materials
Journal of Computational Physics
Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
High order curvilinear finite elements for elastic-plastic Lagrangian dynamics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
We present a new cell-centered Lagrangian scheme on unstructured mesh for hyperelasticity. It is based on the recently proposed Glace scheme [11] for compressible gas dynamics. We show how to use the multiplicative decomposition of the gradient of deformation and the entropy property to derive the new scheme. We also prove the compatibility of this discretization with usual calculations of mass. Our motivation is to use hyperelasticity models for the study of finite plasticity, which is an extension of hypoelasticity to finite deformations. Hyperelasticity is a natural choice for extended models in solid mechanics, because of its mathematical structure which is a system of conservation laws with full rotational invariance. We study these properties for the Lagrangian system, and detail the various Eulerian formulations. We present several test problems, in 1D and 2D planar cases, which shows the capability of the scheme to capture complex shock-waves and to simulate solid-fluid problems. In this article, we use a special equation of state [21]. Its interest is twofold: we can calculate multi-dimensional plastic phenomenon (such as split shock in 1D uniaxial cases or particular shapes in Taylor test-case), and it gives interesting multi-dimensional test cases for hyperelastic planar schemes.