Numerical simulations of the Richtmyer-Meshkov instability in solid-vacuum interfaces using calibrated plasticity laws

Abstract

The Richtmyer-Meshkov instability of interfaces separating elastic-plastic materials from vacuum (heavy-light configuration) is studied by means of computational techniques. A fully Eulerian multimaterial algorithm that solves consistently the Euler equations and the time evolution of the deformations in the material is applied to three distinct materials (copper, aluminum, and stainless steel). If a perfectly plastic constitutive relation is considered, an empirical law is computed that relates the long-term perturbation amplitude of the interface, its maximum growth rate, the initial density, and the yield stress of the material. It is shown that this linear relation can be extended to materials that follow more complex plastic behavior which can account for rate dependency, hardening, and thermal softening, and to situations in which small-perturbation theory is no longer valid. In effect, the yield stress computed from measurements of the long-term amplitude and maximum growth rate closely matches the von Mises stress found at the interface of solid materials for a wide range of cases with different initial parameters.

Numerical Simulations of the Richtmyer–Meshkov Instability of Solid-Vacuum Interface

“…This expression for the relaxation time can be simplified to perfect plasticity in our simulations by setting f H = f T = 1, σ 0 =σ Y , and m 1 high enough so that the equivalent stress σ m conforms to the yield surface defined by σ Y almost immediately. The Godunov-Romenski hyper-elastic constitutive law [15,25] is employed for the modelling of elastic-plastic solids. This closure relation considers contributions to the internal energy related to shear and hydrostatic deformations, respectively:…”

“…[14]. Ortega et al [15] developed an empirical law that relates the long-term perturbation amplitude of the interface, its maximum growth rate, the initial density, and the yield stress of the material by simulating RMI problems with the perfect plastic constitutive relation. Then they extended the empirical law to materials that follow more complex plastic behavior which can account for rate dependency, hardening, and thermal softening, and to situations in which small-perturbation theory is no longer valid.…”

Investigation of the ultrasound-induced collapse of air bubbles near soft materials

“…Recent advancements in the formulation of elasticity in the Eulerian frame [19] , [20] , [21] , [22] , [23] , [24] facilitate its application to FSI problems when combined with a sharp [25] or diffuse interface method [19] (DIM) to include multiple materials. Various works have been published using Eulerian elasticity with sharp interface methods, utilizing the Ghost Fluid Method (GFM) [25] , [26] , [27] or the cut-cell method [28] , [29] , [30] . While these approaches preserve sharp interfaces through complex reconstructions and mixed-cell algorithms they are challenging to implement especially in the case of adaptive mesh refinement (AMR) and introduce non-conservative terms in the case of GFM.…”

Tantalum strength at extreme strain rates from impact-driven Richtmyer-Meshkov instabilities

“…The ability of viscosity to reduce the growth rate of Richtmyer-Meshkov instabilities (RMI) in fluids has been studied for some time [1][2][3][4][5]. The sensitivity of RMI to strength in solids, the analog of viscosity, has received explicit attention more recently [6][7][8][9][10][11][12] with increasing attention also in regard to ejecta [13][14][15][16]. Since the proposal about a decade ago to use RMI to evaluate strength [17,18], several experimental efforts to use this capability have been reported [19][20][21][22][23][24][25][26][27][28][29], although in many cases the experiments serve as validation experiments for strength models rather than providing quantitative estimates of strength.…”