Numerical Modeling of the Nonlinear Elastic Response of Filled Elastomers via Composite-Sphere Assemblages

This paper proposes an effective numerical method to generate approximate solutions for the overall nonlinear elastic response of isotropic filled elastomers subjected to arbitrarily large deformations. The basic idea is first to idealize the random microstructure of isotropic filled elastomers as an assemblage of composite spheres and then to generate statically admissible numerical solutions, via finite elements, for these material systems directly in terms of the response of a single composite sphere subjected to affine stress boundary conditions. The key theoretical strengths of the method are discussed, and its accuracy and numerical efficiency assessed by comparisons with corresponding 3D full-field simulations. The paper concludes with a discussion of straightforward extensions of the proposed method to account for general classes of anisotropic microstructures and filler-elastomer interphasial phenomena, features of key importance in emerging advanced applications.