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

Abstract

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.

Keywords

• Elastic–viscoplastic solids
• Finite volume method
• Flux-difference splitting
• Non-uniform quadrilateral meshes
• Generalized standard materials