Impact of fractional strain on medium containing spherical cavity in the framework of generalized thermoviscoelastic diffusion

Abstract

Viscoelastic materials (elastomers, resins, and polycrystalline metals) are of significant importance due to their numerous applications in biology, civil, and mechanical engineering alongwith other scientific disciplines. Viscoelastic materials possess strong relation with temperature and diffusion phenomenon and their mechanical properties exhibit memory dependence. With this view, fractional order strain is considered to study thermoviscoelastic diffusion interactions in the context of hyperbolic two-temperature-three-phase lag model. The investigation is carried out for an infinite, homogeneous, isotropic medium containing a spherical cavity. Initially, the medium is held quiescent. The boundary of the cavity is subjected to continuous concentration and ramp type thermal load in stress-free state. The problem is solved in Laplace transformed domain. The aim of this article is to analyze the behavior of field variables under thermoelastic models with different fractional order strain, ramping, and viscosity parameters. Physical data of Copper material is considered for numerical inversion technique and obtained results are plotted graphically. Here it is revealed that fractional order strain parameters lead to lower perturbations of stress and viscous effects result in higher temperature. One temperature and hyperbolic two temperature theories produce similar solutions. Ramp type thermal loading at the boundary significantly influences the temporal profile.