Finite thermoelasticity of constrained elastomers subject to biaxial loading

Abstract

Well accepted descriptors of the thermoelastic behavior of elastomers undergoing finite strain remain elusive largely due to the continuing lack of appropriate multiaxial data. In this paper we present a new theoretical framework for inferring thermoelastic constitutive relations directly from biaxial data. In particular, we consider an experimentally natural decomposition of the motion into two parts – one due to traction-free uniform heating and one due to isothermal mechanical loading – and impose a mechanical incompressibility constraint on each motion. It is shown that, regardless of the order of the motions, one obtains a thermoelastic generalization of the classical result of Rivlin and Saunders for identifying response functions from (isothermal) biaxial data.