Analysis of particle-matrix interfacial debonding using the proper generalized decomposition

Syntactic foams are a class of particulate composites consisting of microballoons dispersed in a matrix material. While several modeling schemes have been developed to study their elastic response, the mechanics of failure of these composites is a largely untapped research area. Here, we propose a mathematically tractable framework to analyze particle-matrix interfacial debonding in uniaxial tension. The proper generalized decomposition is used to study the deformation of the matrix and the inclusion, and the method of Lagrange multipliers is adapted to satisfy the boundary conditions along the bonded portion of the inclusion-matrix interface. A variational approach is utilized to derive the governing differential equations, and the Galerkin method is implemented to cast the problem into a manageable set of algebraic equations. An iterative procedure based on the fixed point algorithm is ultimately used to determine the displacement fields. Results are specialized to a glass particle-vinyl ester matrix system, and a parametric study is conducted to understand the mechanics of debonding. Results are validated through available data and new finite element simulations. We find that the proposed framework is in very good agreement with numerical results for a wide range of debonding angles, inclusion volume fractions, and inclusion wall thicknesses.