We investigate the use of combining SIMP topology optimization and phase field method to fracture for maximizing the fracture resistance of a structure composed of two materials. The optimization problem is formulated with respect to maximizing the external work under the constraint of inclusion volume fraction. The performance and convergence of the proposed algorithm are investigated. It is shown that the fracture resistance can be improved as compared to several guess designs with the same volume fraction of reinforcement (inclusion material). A comparison between the present SIMP and BESO methods is performed, showing a better convergence of the SIMP method, more specifically when a homogeneous initial guess design is used. Applications to 2D and 3D composite structure are presented to show the potential and robustness of the approach.

我们研究结合使用SIMP拓扑优化和相场方法来断裂，以使由两种材料组成的结构的断裂抗性最大化。针对夹杂物体积分数约束下的外部工作最大化提出了优化问题。研究了该算法的性能和收敛性。结果表明，与几种具有相同体积分数的增强材料（夹杂材料）的猜测设计相比，可以提高抗断裂性能。进行了当前SIMP方法与BESO方法之间的比较，显示了SIMP方法的更好收敛性，更具体地说，是在使用同质初始猜测设计时。介绍了在2D和3D复合结构中的应用，以显示该方法的潜力和鲁棒性。