The rapid development of additive manufacturing (AM) offers new opportunities to fabricate multi-material structures, whose performance can be optimized by the integrated design of multiple materials distribution and their interface behaviors. However, the graded-interface assumption between different materials often caused some numerical difficulties during topology optimization, e.g., poor applicability in weak interface and difficulty in accurately controlling interface width. This work develops a new element-based topology optimization algorithm by explicitly considering strong, weak or intermediate interfaces, and the interfacial width can also be controlled precisely. Under the explicit expression of a graded interface, a linear multi-material interpolation scheme is proposed to gradually achieve realistic graded physical field within the interfacial zone, where the interdiffusion or reaction inevitably happens and leads to the gradual transition of the interface property. The compliance minimization of multi-material structures with different types of graded interfaces is formulated under multiple volume fraction constraints. The sensitivity of the objective function and constraints with respect to design variables are derived. Numerical examples demonstrate that the optimized designs resulting from the proposed method always achieve a lower compliance, compared with those of the traditional multi-material designs. A phase diagram is presented to describe the sensitivity of the topological design on the interface behavior.

增材制造 (AM) 的快速发展为制造多材料结构提供了新的机会，其性能可以通过多种材料分布及其界面行为的集成设计来优化。然而，不同材料之间的渐变界面假设在拓扑优化过程中经常导致一些数值困难，如弱界面适用性差，界面宽度难以准确控制。这项工作通过明确考虑强、弱或中间界面，开发了一种新的基于元素的拓扑优化算法，并且界面宽度也可以精确控制。在渐变界面的显式表达下，提出了一种线性多材料插值方案，以逐步实现界面区域内真实的渐变物理场，其中不可避免地发生相互扩散或反应并导致界面性质. 具有不同类型渐变界面的多材料结构的柔度最小化是在多个体积分数约束下制定的。导出了目标函数和约束对设计变量的敏感性。数值例子表明，与传统的多材料设计相比，由所提出的方法产生的优化设计总是达到较低的柔顺性。给出了一个相图来描述拓扑设计对界面行为的敏感性。