A unified formulation for thermoviscoelasticity of hollow sphere based on the second sound theories

Abstract

By proposing the unifier factors, a unified formulation for the generalized coupled thermo-visco-elasticity response of hollow spheres based on the Lord–Shulman, Green–Lindsay, and Green–Naghdi models is developed. Kelvin–Voigt model is used in the current research to consider the viscoelastic response of the sphere. This formulation is used to capture the thermoviscoelastic response of finite isotropic hollow sphere under thermal shock. After transforming the one-dimensional radial equations into the non-dimensional form, finite element method (FEM) based on the Galerkin weak formulation is implemented. The governing equations are discretized through the radial domain utilizing FEM. The determined system of ordinary differential equations is traced using the average acceleration method as a type of Newmark time marching scheme. After validation, novel numerical results are demonstrated to analyze the influences of viscoelastic damping on the response of hollow sphere under rapid surface heating based on various types of generalized theories.