Multi-material structural topology optimization considering material interfacial stress constraints

For multi-material structures, ensuring material interface strength is particularly vital for their integrity and durability. In the present study, we incorporate material interfacial stress constraints into topology optimization of bi-material structures. A multi-material level set method, in conjunction with interface-conforming finite element meshes, is employed to describe the distribution of different material phases and to capture the evolution of the material interfaces. The use of interface-conforming meshes enables accurate analysis of both interfacial stresses and their design sensitivities. Noting that the interfacial strength failure is usually characterized by a tension/compression asymmetric mechanism, we adopt an equivalent interfacial stress (which was originally proposed for strength criterion concerning composite delamination) expressed by the interface tensile and tangential stresses in the considered strength criterion. To handle the local nature of such interfacial stress constraints, we propose a global stress measure, which is an approximation of the p-norm of the equivalent interfacial stress field. An adjoint sensitivity analysis scheme is derived by taking into account the interface transmission conditions. To treat multiple constraints (the volume constraints and the interfacial stress constraint) in level set-based topology optimization, the velocity field-level set method is employed. Numerical examples are presented to show effectiveness of the present method. It is also shown that the tension/compression asymmetric interfacial strength criteria may lead to asymmetric designs. (C) 2020 Elsevier B.V. All rights reserved.

对于多材料结构，确保材料界面强度对其完整性和耐久性尤为关键。在本研究中，我们将材料界面应力约束纳入双材料结构的拓扑优化中。采用一种多材料水平集方法，并结合符合界面的有限元网格，来描述不同材料相的分布以及捕捉材料界面的演变。使用符合界面的网格能够对界面应力及其设计灵敏度进行精确分析。注意到界面强度失效通常具有拉/压不对称机制的特征，我们在考虑的强度准则中采用了一种等效界面应力（最初是针对复合材料分层的强度准则提出的），它由界面的拉应力和切应力表示。为了处理这种界面应力约束的局部性质，我们提出了一种全局应力度量，它是等效界面应力场的p -范数的近似值。通过考虑界面传递条件，推导出了伴随灵敏度分析方案。为了在基于水平集的拓扑优化中处理多个约束（体积约束和界面应力约束），采用了速度场 - 水平集方法。给出了数值例子以表明本方法的有效性。还表明拉/压不对称界面强度准则可能导致不对称的设计。（C）2020爱思唯尔有限公司。保留所有权利。