Multiaxial Deformations of End-Linked Poly(dimethylsiloxane) Networks. 1. Phenomenological Approach to Strain Energy Density Function

Abstract

The phenomenological strain energy density function (W) for the elastomeric networks of end-linked poly(dimethylsiloxane) (PDMS) has been investigated as a function of the first and second invariants I1 and I2 of the Green's deformation tensor on the basis of the quasi-equilibrium stress−strain relationships of general biaxial deformations varying independently each of two principal strains. The Ii dependence of ∂W/∂Ij (i,j = 1,2) was obtained from the biaxial stress−strain data using the Rivlin−Saunders method. In the 3-dimensional plots of ∂W/∂Ii (i = 1,2) against both the (I1 − 3)- and (I2 − 3)-axes, the data points of each derivative at large deformations appear to fall on a plane inclining against the (I1,I2) plane, which suggests that both the derivatives linearly depend on each of I1 and I2. The formula of W is reasonably deduced from such linear dependence of ∂W/∂Ii on Ij (i,j = 1,2) as W = C10(I1 − 3) + C01(I2 − 3) + C11(I1 − 3)(I2 − 3) + C20(I1 − 3)2 + C02(I2 − 3)2. Each of the numerical coeffic...