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.

固体的微观结构演化是由不同的因素驱动的，例如熵密度，化学势和机械能。机械能密度随着机械波的传播而传播，这对诸如马氏体相变的快速固态相变具有很大的影响。为了确定在微结构演变过程中对驱动力的机械影响，因此必须模拟多相和多颗粒系统中的机械波传播。通过为每个阶段引入顺序参数，相场方法是一种高效且强大的数值分析工具，它消除了跟踪不同阶段之间的界面的复杂性。本文扩展了相场方法，通过将其与高阶不连续伽勒金耦合来模拟机械波传播方法。尖锐界面处的跳跃条件是针对具有不连续和不连续的机械波得出的。根据跳跃条件，用阶跃参数制定了刚度矩阵和密度的插值方案，以求得微观结构演化的驱动力。进行了数值验证，以验证跳跃条件，插值方案以及该仿真方案的准确性和收敛性。