Eulerian solver for coupled problems of high-speed elastic-plastic deforming inert or reactive materials with a gaseous environment

In this work, we develop a new Eulerian framework for simulations of high-speed elastic-plastic deformations of inert or reactive solid materials coupled with the flow in the surrounding gaseous environment. The governing equations are based on a newly suggested two-phase Wilkins model, for either inert or reactive elastic-plastic materials, with the Johnson-Cook material model. For reactive materials, an exothermic chemical reaction transitions the solid reactants into gaseous products via a simplified Arrhenius chemical kinetics model. The proposed solver uses level-set method for interface tracking with Ghost Fluid Method (GFM) to enforce proper boundary conditions between the deformed elastic-plastic body and the surrounding gaseous environment. For the radial return algorithm used for the elastic-plastic transition, we developed a new iterative-free method. We test our new solver against a variety of existing benchmarks for elastic-plastic problems from the literature. In particular, the classical 1-D Wilkins’ problem. Moreover, for the classical test case of a thick cylindrical or spherical shell collapses, we compare our results to a newly derived semi-analytical solution for the inner and outer radii of the shells as a function of time. Finally, we demonstrate our new framework capability to model both inert and reactive Taylor bar impact tests and extensively compare our numerical results vs existing experimental and numerical data.