A generalized Vlasov-Jones foundation model for micromechanics studies of syntactic foams

Syntactic foams are lightweight particulate composites that are synthesized by dispersing thin hollow inclusions in a matrix material. A spherical elastic inclusion embedded in a dissimilar medium is often used as a unit cell model to study syntactic foams' micromechanics. The analysis of such unit cell problem is generally conducted by modeling both the inclusion and the matrix using three-dimensional linear elasticity. In this paper, we take a different approach by developing a generalized Vlasov-Jones foundation model for the matrix and describing the inclusion using Donnell shell theory. This framework is specialized to uniaxial tensile loading of a spherical matrix in the presence of two equal interfacial cracks introduced to model inclusion-matrix debonding. A variational method is used to formulate a nonlinear boundary value problem for the shell and foundation displacements and an iterative solution procedure based on the Ritz method is presented. For a polymer matrix-glass inclusion system, a parametric study is performed to investigate the effect of debonding extent, inclusion volume fraction, and shell thickness on debonding energetics and effective elastic modulus. The proposed model is validated using finite element results and experimental data on Young's modulus of epoxy-glass syntactic foams.