The concept of the partition of unity (PU) enabled the development of nodal enrichment strategies, such as the Extended Finite Element Method (XFEM) and Generalised Finite Element Method (GFEM), for realistic simulations of structural behaviour with applications to both static and dynamic problems. Nonetheless, the majority of existing methodologies still inherit instability issues for arbitrary discontinuity geometries when using an explicit time integration scheme. To address this, the discrete strong discontinuity approach is herein developed for the simulation of dynamic crack propagation. The formulation is fully variationally consistent and a new mapping approach is introduced to embed the rigid body movements associated with discontinuities while keeping the critical time step bounded. Multiple discontinuities within a single element are also considered for the accurate modelling of crack branching. The stability of the new technique is first verified in one- and two-dimensional elements. Next, the accuracy and efficiency are validated with structural examples including tensile and mixed-mode loadings. A concrete L-specimen, where different loading rates produce significant variations in failure patterns and strength, is also considered. Results show the good overall agreement with experimental data and other numerical studies available in the literature. The new formulation, however, is able to capture complex crack propagation phenomena, such as crack branching, without any specific additional criterion (e.g. based on crack tip velocity). The formulation presented in this paper is, to the best of the authors’ knowledge, the first PU-based consistent finite element with intrinsically bounded critical time step for explicit time integration.

统一分区（PU）的概念使节点富集策略的发展成为可能，例如扩展有限元方法（XFEM）和广义有限元方法（GFEM），用于结构行为的真实模拟以及静态和动态应用问题。但是，当使用显式时间积分方案时，大多数现有方法仍会继承任意不连续几何的不稳定性问题。为了解决这个问题，本文开发了离散的强不连续方法来模拟动态裂纹扩展。该公式在变化上是完全一致的，并且引入了一种新的映射方法来嵌入与不连续相关的刚体运动，同时保持关键的时间步长为界。单个元素内的多个不连续性也被考虑用于裂纹分支的精确建模。首先在一维和二维元素中验证了新技术的稳定性。接下来，通过包括拉伸和混合模式载荷在内的结构示例验证了精度和效率。还考虑了一个具体的L形试样，其中不同的加载速率会导致破坏模式和强度发生显着变化。结果表明与文献中提供的实验数据和其他数值研究具有良好的总体一致性。然而，新的公式能够捕获复杂的裂纹扩展现象，例如裂纹分支，而无需任何特定的附加标准（例如，基于裂纹尖端速度）。据作者所知，本文提出的表述是，