Interfaces between structural multi-materials generally exhibit asymmetric resistance to tension and compression. Given this interface behavior, this work suggests an energy-based approach to improve the interface configuration for multi-material topology optimization. Based on the strain spectral decomposition, we decompose the structural elastic strain energy into tensile and compressive portions. In the density-based topology optimization framework, we use the gradient-based method to track the interface between multiple materials. Then, we construct an interface-associated scalar field to penalize the tensile portion of the strain energy, causing a pseudo-degradation of the strain energy at the interface region. Finally, within limited material usages and by minimizing the linear weighted structural strain energy and its pseudo-degradation, multi-material topology optimization with improved interface configuration is achieved. Several 2D and 3D numerical examples are investigated, by which the effectiveness and robustness of the suggested approach are fairly validated.

中文翻译：

---

通过改进界面配置将界面效应纳入多材料拓扑优化：基于能量的方法


结构性多材料之间的界面通常表现出不对称的抗拉和抗压能力。鉴于这种界面行为，这项工作提出了一种基于能量的方法来改进多材料拓扑优化的界面配置。基于应变谱分解，我们将结构弹性应变能分解为拉伸和压缩部分。在基于密度的拓扑优化框架中，我们使用基于梯度的方法来跟踪多种材料之间的界面。然后，我们构造一个与界面相关的标量场来惩罚应变能的拉伸部分，导致界面区域应变能的伪退化。最后，在有限的材料使用范围内，通过最小化线性加权结构应变能及其伪降解，实现了具有改进的界面配置的多材料拓扑优化。研究了几个 2D 和 3D 数值示例，所提出方法的有效性和鲁棒性得到了相当的验证。