Simulation of impacts on elastic\u2013viscoplastic solids with the flux-difference splitting finite volume method applied to non-uniform quadrilateral meshes

Thomas Heuzé

doi:10.1186/s40323-018-0101-z

Abstract

The flux-difference splitting finite volume method (Leveque in J Comput Phys 131:327–353, 1997; Leveque in Finite volume methods for hyperbolic problems. Cambridge: Cambridge University Press, 2002) is here employed to perform numerical simulation of impacts on elastic–viscoplastic solids on bidimensional non-uniform quadrilateral meshes. The formulation is second order accurate in space through flux limiters, embeds the corner transport upwind method, and uses a fractional-step method to compute the relaxation operator. Elastic–viscoplastic constitutive models falling within the framework of generalized standard materials (Halphen and Nguyen in J Mech 14:667–688, 1975) in small strains are considered. Many test cases are proposed and two particular viscoplastic constitutive models are studied, on which comparisons with finite element solutions show a very good accuracy of the finite volume solutions, both on stresses and viscoplastic strains.

Highlights

The numerical simulation of hyperbolic initial boundary value problems including extreme loading conditions such as impacts requires the ability to accurately capture and track the fronts of shock waves induced in the medium
Numerical schemes able to represent regular as well as discontinuous solutions are of interest; more precisely, they should meet both high orders of accuracy in regions where the solution is smooth and a high resolution of discontinuities when they occur without any numerical spurious oscillations appearing in their vicinity
The elastic–viscoplastic system of equations identifies itself with a relaxation system with threshold, whose asymptotic limit yields an elastic–plastic system

Summary

Introduction

The numerical simulation of hyperbolic initial boundary value problems including extreme loading conditions such as impacts requires the ability to accurately capture and track the fronts of shock waves induced in the medium. Properties of numerical schemes A system of hyperbolic conservation laws with relaxation is said to be stiff when the relaxation time τ is small compared to the time scale determined by the characteristic speeds of the system and some appropriate length scales [42], or put in another way, the wave-propagation behavior of interest occurs on a much slower time scale than the fastest time scales of the ordinary differential equation (ODE) arising from the source term.

Results

Conclusion