Tempered fractional MGT thermoelasticity in a transversely isotropic medium with temperature-dependent properties

Abstract

Many materials and physical systems show memory effects that gradually weaken with time but strongly influence their transient response, as seen in viscoelastic and thermoelastic materials. Tempered fractional operators provide an effective framework for capturing this behaviour by combining power-law memory with a natural exponential decay. Building on this idea, the present work develops a tempered fractional Moore–Gibson–Thompson (TFMGT) thermoelastic formulation to analyse the transient behaviour of a transversely isotropic medium with temperature-dependent material properties. The novelty of the present study lies in incorporating the tempered fractional operator and a two-dimensional (2D) transversely isotropic cylindrical medium within the considered framework. The medium is initially at rest and subjected to a ramp-type thermal load under traction-free boundary conditions. Temperature-dependent thermal and elastic parameters are included in the governing relations, leading to a strongly coupled thermomechanical system. The governing equations are non-dimensionalized and analytically solved in the Laplace–Hankel transform domain, and a numerical inversion technique is applied to obtain the physical responses for cobalt material. The results show that the fractional-order and tempering parameters significantly influence the overall spread of thermal and mechanical disturbances. The temperature-dependent parameter further intensifies coupling effects, altering the amplitude of field variables. The study provides a unified theoretical basis for examining memory-driven thermoelastic behaviour and offers guidance for designing materials with controlled thermal performance under transient loading.