Advances in the computational modeling of fracture of solids have opened up new possibilities for structural design optimization to enhance fracture properties. Here, we investigate material optimization and design to improve fracture behavior of composite structures under quasi-static conditions. The rate-independent structural problem considering cohesive fracture is ill-posed in its original form due to the non-unique nature of the solution. This renders the use of gradient-based optimization algorithms problematic. To overcome this issue, we introduce viscous regularization and a local approximation of the cohesive law into the governing state equations, and study the impact with the help of interfacial fracture of composite structures consisting of two or more materials. The fracture problem is then integrated into a material optimization framework. We study the effect of viscous regularization on the global landscape of the proposed objective function using a 2-dimensional delamination example with one design parameter and discuss difficulties resulting from the stabilization of inherently unstable crack states. In view of these issues, we finally propose considering multiple state problems, each limited to a single crack, with different predefined crack paths. In the end, we optimize the orientations of orthotropic inclusions embedded in a double-cantilever beam for the worst case of the potential crack paths.

固体断裂计算模型的进展为结构设计优化以增强断裂性能开辟了新的可能性。在这里，我们研究材料的优化和设计，以改善准静态条件下复合结构的断裂行为。由于溶液的非唯一性质，考虑到内聚破裂的与速率无关的结构问题是不恰当的。这使得基于梯度的优化算法的使用成为问题。为了克服这个问题，我们引入了粘性正则化并将内聚律的局部近似值转化为控制状态方程，并借助两种或多种材料组成的复合结构的界面断裂来研究其影响。然后将断裂问题整合到材料优化框架中。我们使用二维研究粘性正则化对拟议目标函数的整体格局的影响一个设计参数的分层示例，并讨论了固有不稳定裂纹状态的稳定所带来的困难。鉴于这些问题，我们最终提出考虑具有不同预定义裂纹路径的多个状态问题，每个状态问题仅限于单个裂纹。最后，针对潜在裂纹路径的最坏情况，我们优化了双悬臂梁中嵌入的正交各向异性夹杂物的取向。