The Theories of Rubber Elasticity and the Goodness of Their Constitutive Stress–Strain Equations

Abstract

One of the most important challenges in polymer science is a rigorous understanding of the molecular mechanisms of rubber elasticity by relating macroscopic deformation to molecular changes and deriving the constitutive stress–strain equation for the elastomeric network. The models developed from the last century to today describe many aspects of the physics of rubber elasticity; although these theories are successful, they are not complete. In this review we analyze the main theoretical and phenomenological models of rubber elasticity, including their assumptions, main characteristics, and stress–strain equations. Then, we compare the predictions of the theories to our experimental data of polydimethylsiloxane (PDMS) rubber, in order to highlight the goodness of the reviewed models. The nonaffine and phenomenological deformation models verify the experimental curves in tension and compression in the whole investigated deformation range λ≤2. On the contrary, the affine deformation hypothesis is rigorously verified only in the deformation range λ≤1.

Keywords

• rubber elasticity models
• constitutive stress–strain equations
• affine deformation
• nonaffine deformation
• ideal rubbers
• tube models