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

Abstract

It is important to study the fundamental deformation behaviour, especially the nonuniform distribution of stress and strain in the rubber composite material. In the present paper, tensile deformation of the rubber composite material under the condition of plane strain is analysed numerically with the Mooney-Rivlin-type strain energy function. Namely, a plane model of in-homogeneous material is adopted as a model of a rubber composite material. Ellipsoidal inclusions with different elastic constant are assumed to be placed regularly in the matrix. The problem of the incompressibility of rubber is treated using the penalty function in the finite-element formulation. The incremental load method and Newton-Raphson's method are used for the numerical calculation of the nonlinear problem. It is found that the deformation of the model comes to have a similar mode with that of constant strain as the shape of the inhomogeneous region becomes slender in the stress direction. The distribution of stress and strain in the inclusion is nearly constant.