Journal of Computational Physics
An upwind second-order scheme for compressible duct flows
SIAM Journal on Scientific and Statistical Computing
Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations
SIAM Journal on Scientific and Statistical Computing
The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
Journal of Computational Physics
A high-order Eulerian Godunov method for elastic-plastic flow in solids
Journal of Computational Physics
A free-Lagrange augmented Godunov method for the simulation of elastic-plastic solids
Journal of Computational Physics
Journal of Computational Physics
Remark on the generalized Riemann problem method for compressible fluid flows
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
Short Note: Volume consistency in a staggered grid Lagrangian hydrodynamics scheme
Journal of Computational Physics
Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics
Journal of Computational Physics
Journal of Computational Physics
An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids
Journal of Computational Physics
Discretization of hyperelasticity on unstructured mesh with a cell-centered Lagrangian scheme
Journal of Computational Physics
Diffuse interface model for compressible fluid - Compressible elastic-plastic solid interaction
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic-plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.