Computational Physics Group

Karel Matous









Finite element formulation for modeling particle debonding in reinforced elastomers subjected to finite deformations

K. Matous and P.H. Geubelle

Center for Simulation of Advanced Rockets
Department of Aerospace Engineering
University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA.


Interfacial damage nucleation and evolution in reinforced elastomers is modeled using a three-dimensional updated Lagrangian finite element formulation based on the perturbed Petrov-Galerkin method for the treatment of nearly incompressible behavior. The progressive failure of the particle-matrix interface is modeled by a cohesive law accounting for mode mixity. The meso-scale is characterized by a unit cell, which contains particles dispersed in a homogenized blend. A new, fully implicit and efficient finite element formulation, including consistent linearization, is presented. The proposed finite element model is capable of predicting the non-homogeneous meso-fields and damage nucleation and propagation along the particle-matrix interface. Simple deformations involving an idealized solid rocket propellant are considered to demonstrate the algorithm.


We have formulated and implemented a 3D computational model to simulate dewetting evolution in reinforced elastomers subject to finite strains. The particle-matrix interface is modeled by a cohesive law that accounts for irreversibility and mode mixity. The finite element framework is based on a stabilized updated Lagrangian formulation and adopts a decomposition of the pressure and displacement fields to eliminate the volumetric locking due to the nearly incompressible behavior of a matrix. The consistent linearization of the resulting system of nonlinear equations has been derived and leads to an efficient solution of the complex highly nonlinear problem. Through a set of examples involving one- and four-particle unit cells, we have shown the ability of the numerical scheme to capture the non-homogeneous stress and deformation fields present in the matrix and the damage nucleation and propagation along the particle-matrix interface. In particular, the scheme was shown to capture effects associated with the interface strength and nonuniform particle spacing and size. The existence of a bifurcation in the solution path was also briefly investigated. The present work is a first step toward linking the macro-scale to the meso-scale through the computational homogenization, where a meso-structure is fully coupled with the deformation at a typical material point of a macro-continuum. The formulation and implementation of a truly multiscale model for the effect of microstructural damage on the macroscopic constitutive response of reinforced elastomers is the topic of our future research.


The authors gratefully acknowledge support from the Center for Simulation of Advanced Rockets (CSAR) at the University of Illinois, Urbana-Champaign. Research at CSAR is funded by the U.S. Department of Energy as a part of its Advanced Simulation and Computing (ASC) program under contract number B341494.
© 2009 Notre Dame and Dr. Karel Matous