In the automotive industry, crack prediction is an important step of the design: its accuracy is crucial to avoid additional development costs and delays. However, its simulation is not always reliable yet which could be explained by the use of too simple fracture criteria. A possible solution could be the improvement of the fracture behavior prediction through the use of coupled damage models. Unlike the fracture criteria, damage models consider the loss of resistance on the elements behavior, which gives a better definition of the strain localization and crack path. However, due to stress softening, the problem becomes ill posed, generating damage localization on a single row of elements. The results are then dependent on the mesh size and the mesh orientation. To obtain mesh independent results, a possible solution is to resort to regularization methods, but only a few of them are compatible with dynamic explicit simulations, especially for ductile failure. This paper proposes to extend the implicit second gradient non-local regularization approach to crash simulations. This is achieved by modifying the second gradient equation to ensure its robustness for dynamic explicit simulations. This extended second gradient approach is implemented by enriching under-integrated continuum elements so as to naturally preserve the parallel computing ability. A comparison between simulations and experimental results obtained with specimens machined in a dual-phase steel sheet is realized to validate the proposed approach. Numerical results obtained with different mesh sizes and mesh orientations illustrate the mesh independence and are in very good agreement with the experiments in terms of both load–displacement curves and crack path.

在汽车行业，裂纹预测是设计的重要步骤：其准确性对于避免额外的开发成本和延迟至关重要。然而，它的模拟并不总是可靠的，这可以通过使用过于简单的断裂标准来解释。一种可能的解决方案是通过使用耦合损伤模型来改进断裂行为预测。与断裂标准不同，损伤模型考虑了元素行为的阻力损失，从而更好地定义了应变局部化和裂纹路径。然而，由于应力软化，问题变得不适定，在单行单元上产生损伤定位。结果取决于网格大小和网格方向。为了获得网格无关的结果，一种可能的解决方案是采用正则化方法，但只有少数方法与动态显式模拟兼容，尤其是对于延性破坏。本文提出将隐式第二梯度非局部正则化方法扩展到碰撞模拟。这是通过修改第二个梯度方程来实现的，以确保其对动态显式模拟的鲁棒性。这种扩展的第二梯度方法是通过丰富欠集成的连续元素来实现的，从而自然地保留并行计算能力。通过在双相钢板中加工的试样获得的模拟和实验结果之间的比较被实现以验证所提出的方法。