Numerous topology optimization formulations have been proposed in order to enhance structural resistance to material failure. A clear line can often be drawn between those methods which attempt to constrain local failure criteria and those that explicitly model the failure physics during the optimization process. In this work the former method is extended in a manner inspired by the mathematical form of typical gradient-enhanced damage models. Importantly, the proposed formulation relies on linear physics during the optimization procedure, which greatly increases its speed and robustness, both of which are essential in industrial applications where large numerical models are typically used. The size effect introduced by using such a numerical model is further investigated and select observations are provided, such as spurious “fin-like” patterns that emerge depending on the type of structure and loading conditions. Finally, the load capacity is verified for each optimized design through a post-optimization verification procedure which is unaffected by the density-based design parameterization and associated material interpolation schemes.

为了增强结构对材料失效的抵抗力，已经提出了许多拓扑优化公式。通常可以在那些试图约束局部失效标准的方法和那些在优化过程中明确模拟失效物理的方法之间划清界限。在这项工作中，前一种方法的扩展方式受到典型梯度增强损伤模型的数学形式的启发。重要的是，所提出的公式在优化过程中依赖于线性物理，这大大提高了它的速度和鲁棒性，这两者在通常使用大型数值模型的工业应用中都是必不可少的。进一步研究了使用这种数值模型引入的尺寸效应，并提供了选择的观察结果，例如根据结构类型和负载条件出现的虚假“鳍状”图案。最后，通过优化后验证程序验证每个优化设计的负载能力，该程序不受基于密度的设计参数化和相关材料插值方案的影响。