Multiple scales homogenisation of a porous viscoelastic material with rigid inclusions #

Andres F Galvis, J M Foster, Bartosz Protas, Stephen J Chapman

11:50 Monday in 2Q48.

Part of the Mechanics of hydrogels and poroelastic media session.

Abstract #

This work presents the analysis of the mechanical behaviour of the electrode composite structures in lithium-ion batteries. These are relatively high modulus active particles inclusions within a two-component matrix of liquid electrolyte which penetrates the pore space within a viscoelastic polymer binder. Deformation of the composite is driven by a combination of (i) swelling/contraction of the electrode particles in response to lithium insertion/extraction, (ii) swelling of the binder as it absorbs electrolyte, and (iii) external loading. We derive the macroscale effective response of the composite using multiple scales homogenisation by exploiting the disparity in length scales associated with the size of the electrode particles and the electrode as a whole. The results of this homogenisation procedure are a set of effective differential equations and a new constitutive relationship for the description of the effective material at the macroscale. In order to check the feasibility of our macroscopic model, we compare its results to numerical problems of battery applications.