A computational homogenisation approach for viscoelastic composites with general imperfect interfaces

In polymer nanocomposites, the effective viscoelastic response is strongly influenced by nanoscale confinement and interfacial effects stemming from matrix–filler interactions. In such systems, polymer chain mobility near matrix–filler interfaces deviates from bulk behaviour, leading to non-classical energy storage and dissipation mechanisms that are not captured by classical homogenisation approaches. Hence, accurately linking microscale interfacial mechanisms to macroscopic, frequency-dependent material properties remains a significant challenge. Motivated by these limitations, a computational homogenisation framework for viscoelastic composites with general imperfect interfaces is proposed. The microscale response is described by using sharp interface formulations that admit displacement and traction jumps as well as in-plane surface deformation and tangential transport processes along the interface. By invoking the viscoelastic correspondence principle, the time-dependent problem is transformed into an equivalent frequency-domain formulation with complex-valued constitutive operators. Based on this representation, a multiscale framework satisfying the Hill–Mandel energy equivalence is developed to link viscoelastic microscale interface mechanisms to macroscopic effective moduli. The proposed formulation is examined through detailed analyses of representative boundary value problems, including analytical and numerical homogenisation of periodic microstructures. The results quantify the influence of cohesive and elastic interface parameters on the effective storage and loss moduli across a wide frequency range.