Hyperelastic large deformations of two-phase composites with membrane-type interface

Abstract

The composite under investigation consists of two phases which are bonded together through a membrane-type interface. The work reported in this paper aims at studying the hyperelastic large deformations of this composite while accounting for interfacial stress effects. A variational formulation for a general traction boundary value problem of the composite is provided, leading to the local bulk and interfacial equilibrium equations and to the traction boundary conditions. Assuming that each bulk phase is incompressible and characterized by an energy density function depending only on the trace of the right Cauchy–Green bulk strain tensor and that the interface is compressible and defined by an energy density function being isotropic with respect to the right Cauchy–Green surface strain tensor, exact solutions are given for the simple axial extension, simple torsion and out-of-plane shear of a fiber-reinforced cylinder, and a closed-form solution is also found for a hollow composite sphere subjected both to an internal pressure and an external pressure. These analytical results are further specified and discussed in the particular case where each bulk phase is described by an incompressible Neo–Hookean law and the interface is specified by a compressible Neo–Hookean law. Apart from their own usefulness, the results obtained in this work can serve as benchmarks for relevant numerical methods.