Cohesive-frictional interphase failure modeling for multi-material topology optimization

This work presents a cohesive-frictional interphase failure modeling approach for density-based multi-material topology optimization. As the multi-phase transition region is naturally represented as a finite-thickness interphase within the density-based framework, we assess its failure state directly using principal stresses and stress invariants. Accordingly, a dual-criterion formulation is proposed, which combines the Drucker–Prager criterion for pressure-sensitive shear strength with the Rankine criterion for tensile strength. A thin-layer reduction further connects the formulation to classical traction-based descriptions in the thin and compliant interphase limit. Since the strength assessment is performed directly in the multiaxial stress space, no explicit geometric normal tracking or traction projection is required. The formulation is then incorporated into the density-based topology optimization problem, with morphological interphase extraction, q – p stress relaxation, and self-normalized Softmax aggregation employed in the numerical implementation. Two- and three-dimensional examples demonstrate that the proposed interphase strength formulation effectively relocates the interphase from tensile- and shear-dominated regions toward compression-dominated regions, thereby reducing the corresponding failure indices. Comparative cohesive zone model re-analyses further show that the optimized designs exhibit improved resistance to damage-induced degradation of load-carrying capacity.