Numerical Analysis of Deformation of Rubber Composite Material : Tensile Deformation under Plane Strain

Abstract

The fundamental deformation behaviour of rubber composite material, especially the nonuniform distribution of stress and strain, is studied. Tensile deformation of rubber composite material under the condition of plane strain is analysed numerically using the Mooney-Rivlin-type strain energy function. A planar model of in-homogeneous material is adopted as a model of the rubber composite material. Elliptic rubber inclusions with different elastic constants are assumed to be placed regularly in the matrix rubber. The problem of the incompressibility of rubber is treated, adopting the penalty function method in the finite-element analysis. The incremental load is applied and Newton-Raphson's method is used for the repeated numerical calculation of the nonlinear problem. It is found that the deformation of the composite model becomes similar to that under constant strain when the shape of the inhomogeneous region becomes slender in the stress direction. The distribution of stress and strain in the elliptic inclusion is nearly constant.