Simulating mechanical wave propagation within the framework of phase-field modelling

The microstructural evolution in solids is driven by different factors, such as entropy density, the chemical potential and mechanical energy. The mechanical energy density propagates along with the propagation of the mechanical wave, which has a great influence on the rapid solid-state phase transformation, such as the martensitic transformation. In order to determine the mechanical contribution to the driving force during the microstructural evolution, it is therefore indispensable to simulate the mechanical wave propagation within a multiphase and multigrain system. With the introduction of an order parameter for each phase, the phase-field method is an efficient and robust numerical analysis tool, which obviates the complexity of tracking the interfaces among different phases. In this paper, the phase-field method is extended to simulate the mechanical wave propagation by coupling it with the high-order discontinuous Galerkin method. The jump condition at the sharp interface is derived for mechanical waves with strong and weak discontinuities. Based on the jump condition, the interpolation scheme for the stiffness matrix and the density is formulated with order parameters, so as to derive the driving force for the microstructural evolution. Numerical validations are carried out to verify the jump condition, the interpolation scheme and the accuracy and convergence of this simulation scheme.