An extended Mori-Tanaka homogenization scheme for finite strain modeling of debonding in particle-reinforced elastomers

In the present study, the strength and failure of elastomeric composites are predicted by extending the Mori and Tanaka [T. Mori, K. Tanaka, Acta Metallurgica 21 (1973) 571-574] model from the case of perfectly adherent, linear elastic constituents to the case of nonlinear (hyperelastic) constituents subjected to particle debonding. A finite strain formalism is adopted, and an exponential cohesive zone model is used at the particle-matrix interface. Instead of relying on Eshelby's solution, the isolated inclusion problem is solved numerically using a finite element discretization. The proposed homogenization scheme is applied to a solid propellant in which the particles are much stiffer than the matrix. The analysis is performed in plane strain under axisymmetric tensile loading conditions, and the predictions are compared to reference full-field solutions obtained by finite element simulations on unit cells with periodic boundary conditions. It is demonstrated that the new method yields acceptable predictions until the onset of damage, while dramatically reducing the computational time.