Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations

Interfacial damage nucleation and evolution in reinforced elastomers subjected to finite strains is modelled using the mathematical theory of homogenization based on the asymptotic expansion of unknown variables. The microscale is characterized by a periodic unit cell, which contains particles dispersed in a blend and the particle matrix interface is characterized by a cohesive law. A novel numerical framework based on the perturbed Petrov–Galerkin method for the treatment of nearly incompressible behaviour is employed to solve the resulting boundary value problem on the microscale and the deformation path of a macroscale particle is predefined as in the micro-history recovery procedure. A fully implicit and efficient finite element formulation, including consistent linearization, is presented. The proposed multiscale framework is capable of predicting the non-homogeneous microfields and damage nucleation and propagation along the particle matrix interface, as well as the macroscopic response and mechanical properties of the damaged continuum. Examples are considered involving simple unit cells in order to illustrate the multiscale algorithm and demonstrate the complexity of the underlying physical processes