Homogenised properties of composites with spring-type imperfect contact and inelastically evolving constituents

This work presents a homogenisation framework for determining the effective mechanical properties of two-phase composites with spring-type imperfect contact whose constituents undergo internal structural evolution. The latter is described within the framework of the multiplicative decomposition of the deformation gradient, accounting for inelastic distortions in each constituent phase. The interaction between the phases is modelled through a spring-type imperfect interface, which allows for displacement discontinuities while maintaining traction continuity across the interface. An asymptotic homogenisation approach is used to derive the macroscopic balance equations together with the corresponding effective coefficients. The general formulation is specialised to periodically laminated composites, leading to explicit analytical expressions for the effective mechanical properties of the homogenised system. These expressions capture the combined influence of elasticity, remodelling-induced inelastic effects, and interfacial stiffness. Finally, by considering a representative remodelling law, we solve the resulting coupled homogenised system in a simplified one-dimensional setting. The results illustrate the influence of remodelling and interfacial stiffness on the homogenised response, showing time-dependent effective coefficients and a nonlinear macroscopic displacement, and recover the perfect-contact case as a limiting case.