Eigenstate-based homogenization for inelastic heterogeneous media with imperfect interfaces

This work extends eigenstate-based homogenization (EBH), previously formulated for perfectly bonded interfaces, to general heterogeneous composites with imperfect, damageable interfaces. The resulting framework captures coupled bulk inelasticity and interfacial damage evolution within a unified EBH formulation. A key feature of the proposed framework is its minimal representation of the fine-scale RVE solution: both bulk and interface nonlinearities are described by scalar eigenstates associated with precomputed coarse eigenmodes. Built on transformation field analysis, the formulation accurately recovers both homogenized and fine-scale fields using far fewer unknowns than the full finite element discretization. The central computational obstacle in extending EBH to imperfect interfaces is the severe ill-conditioning induced by penalty-based cohesive zone models. This poor conditioning makes monolithic fixed-point iterations, which are highly efficient for bulk inelasticity alone, prohibitively slow once interfacial damage initiates. To overcome this challenge, we develop a block FP–DR scheme: the well-conditioned bulk inelasticity problem is solved by fixed-point (FP) iterations, whereas the ill-conditioned interface damage problem is solved by Newton iterations combined with LU decomposition for the dense linearized systems of equations, herein referred to as the DR solver. Convergence studies are conducted for both monolithic and block solution schemes. The results show that convergence of the monolithic FP solver depends strongly on the interface regularization and is no longer guaranteed once a critical damage level is reached. In contrast, although the convergence rate of the block EBH schemes remains affected by the maximum interface damage and the interface regularization, these quantities no longer constitute necessary conditions for convergence. Exploiting the rapid initial convergence observed in monolithic FP solvers for bulk inelasticity, we further introduce a loosely converged block EBH variant that achieves significant computational speedup without sacrificing solution accuracy. Numerical studies on fiber-composite and polycrystalline rock RVEs demonstrate that the proposed EBH framework, particularly the block schemes, delivers high-fidelity multiscale predictions for diverse interface-dominated problems at a small fraction of the computational cost of full finite element analysis.