Numerical simulations of elastic-plastic Richtmyer-Meshkov instability of multiple interfaces

The elastic-plastic Richtmyer-Meshkov instability of multiple interfaces is investigated by numerical simulation using a multimaterial solid mechanics algorithm based on an Eulerian framework. This Richtmyer-Meshkov instability problem is realized by a copper layer that is flanked by vacuum and a copper block of different material strength. The research efforts are directed to reveal the influence of the layer thickness and material strength on the deformation of the perturbed solid-vacuum interface impacted by an initial shock. By varying the initial thickness (x_{I}) of the copper layer and the yield stress (σ_{Y2}) of the copper block, two deformation modes, which have been identified as the broken mode and the stable mode, are closely scrutinized. For a fixed x_{I} and a decreasing σ_{Y2}, the reflected rarefaction waves (RRWs), developing after the initial shock impacts the perturbed interface 1 (I1) between vacuum and the copper layer, become stronger after traveling across the interface 2 (I2). Subsequently, the velocity of I2 becomes larger, causing the width of I1 to grow larger. This width growth of I1 leads to a final separation of the spike from I1 and, consequently, the deformation mode changes from the stable mode to the broken mode. For a fixed σ_{Y2} and a decreasing x_{I}, the RRWs impact I2 at an earlier moment with a greater strength and thus the deformation mode changes from the stable mode to the broken mode. Meanwhile, the comparison of the spike width of cases whose deformation mode is the broken mode shows that there exists a maximum value of rescaled spike width, at which the deformation mode changes from the stable mode to the broken mode.