Thermohyperelastic constitutive response for semilinear materials with application to deformation of a rotating thin disk

Abstract

Constitutive modeling of soft elastomers is a well researched subject due to its numerous engineering applications. This study derives a thermodynamically consistent constitutive model for semilinear thermoelastic solids for which the strain energy density depends on the deformation gradient through the Biot stretch tensor. The Frechet derivatives, Coleman-Noll procedure, and product decomposition-based technique are employed to formulate the constitutive model. The combination of the derived model and thermomechanical field equations is specialized for application to problem of radial deformation of a rotating thin disk. The formulated model provides simple closed-form expressions for simulating thermomechanical responses of solids. Under suitable conditions, the derived three-configuration-based constitutive model reduces to the two-configuration-based constitutive equations. Finally, and among other things, the numerical solutions illustrate the effects of angular speed of rotation on thermal stress and displacement fields at points within the radially deforming rotating disk.