Upscaling elastic interphases to canonical interface models

Finite-thickness interphases in heterogeneous materials are often idealized as zero-thickness interfaces in computational models. The interphase may be for instance the transition zone between inclusion and matrix in composites or the grain boundaries in polycrystalline solids. A more advanced application arises in the context of batteries, where the solid electrolyte interphase forms an electro-chemo-mechanically active layer surrounding the electrodes. For geometrically equivalent macro samples, due to increasing area-to-volume ratio with decreasing size, including interfaces introduces a length-scale into the effective response of heterogeneous materials. Recently, a canonical interface model was proposed by the authors that permits both displacement and stress discontinuities across the interface. Unlike the general interface model, this framework treats the interface displacement as an independent field with its own constitutive behavior. However, the associated interface parameters remain phenomenological to date. In this paper, we account for the microstructural features in a thin interphase zone and employ out-of-plane geometrical reduction together with variationally consistent InterPhase Homogenization (IPH) in order to derive the interface properties. In other words, phenomenological parameter values are replaced by “physics-based” values. In particular, it is possible to account for any complex micro-design within the interphase to bring about metamaterial characteristics upon upscaling. Numerical results showcase the upscaled response and highlight the significance of the microstructural design and constitutive relations of the interphase pertinent to a multiphase elastic solid.