A fluid-solid diffuse interface model with phase field for compressible viscoplastic flows

Important difficulties exist with conventional approaches coupling fluid and solid mechanics, e.g, Arbitrary Lagrangian Eulerian methods. A fully Eulerian diffuse interface model for the representation of an arbitrary number of fluids and solid phases is extended to include the phase field mechanism that allows for the preservation of an interface of given thickness between phases over the duration of the computation. Variations in material properties in the equation of state and constitutive model enable a representation of gases, liquids, and solids in a unified framework. The phase field mechanism is based on the conservative Allen-Cahn formulation and its combination with a plastic relaxation step allows to accurately identify each phase, and, especially, permanent deformations imparted to solids. The resulting model is hyperbolic, consistent, conservative, and suitable for high-rate phenomena. We apply the model to study the inertial collapse of a gas bubble immersed in water and near a steel boundary. Our studies focus on permanent deformations induced to the solid surface by the shock waves generated by the collapsing bubble.