We present a new numerical approach for wave induced dynamic fracture. The method is based on a discontinuous Galerkin approximation of the first-order hyperbolic system for elastic waves and a phase-field approximation of brittle fracture driven by the maximum tension. The algorithm is staggered in time and combines an implicit midpoint rule for the wave propagation followed by an implicit Euler step for the phase-field evolution. At fracture, the material is degraded, and the waves are reflected at the diffusive interfaces. Two and three-dimensional examples demonstrate the advantages of the proposed method for the computation of crack growth and spalling initiated by reflected and superposed waves.

翻译：我们为波引动动态骨折提出了一个新的数字方法。该方法基于弹性波第一阶双曲系统不连续的Galerkin近似值,以及由最大张力驱动的骨质骨折的相近值。算法是时间错开的,并结合了波传播的隐含中点规则,然后是相向场演变的隐含电动步骤。在骨折时,材料会降解,波波会反射到 diffusive 界面。两维和三维例子显示了拟议方法的优点,用于计算由反射和被覆盖的波引发的裂纹生长和冲击。