Multi-material topology optimization with interfacial stress constraints using body-fitted IGA

Abstract This work presents a multi-material topology optimization method that incorporates interfacial stress constraints accurately. Using a precise boundary representation that is body-fitted to the evolving optimized topology, direct evaluations and control of both normal and shear stresses at material boundaries are achieved. Consistent sensitivity analysis is conducted following a discretize-then-differentiate approach, and optimization is performed using sequential convex programming. The method yields smooth, CAD-compatible geometries that reduce interfacial stress concentrations without the need for post-processing or artificial regularization. Several numerical examples demonstrate the capability of the framework to balance interfacial stresses with structural stiffness, while the optimized outcomes clearly exhibit the adaptation of the boundary to the allowable level of stress. Overall, the method provides a credible and physically consistent tool for structural design in boundary-sensitive, multi-material applications.