Weighted eigenseparation-based residual approach for model reduction of interface failure in heterogeneous materials

Abstract

Interface failure plays a critical role in the degradation of heterogeneous materials, often governing structural integrity across a range of applications from fiber-reinforced composites to polycrystalline rocks. This paper introduces a novel model reduction framework—the Weighted Eigenseparation-based Residual (WER) approach—for efficiently simulating interface failure using cohesive zone models. Two variants of the WER are developed: a force-based formulation that weakly enforces equilibrium equations at the interface at the modal level and a separation-based formulation that weakly enforces contact conditions at the modal level. These formulations are supported by precomputed influence functions within representative volume elements (RVEs), significantly reducing computational cost while preserving accuracy. The separation-based variant, in particular, demonstrates broad applicability across microstructures with interface junctions. Numerical examples in two and three dimensions—including fiber composites and geological microstructures—demonstrate the effectiveness, convergence behavior, and computational advantages of the WER over direct numerical simulations. The results show that high-fidelity predictions can be obtained even with coarsely discretized interface modes, confirming the robustness and versatility of the WER methodology.