State–space approach on two-temperature three-phase-lag thermoelastic medium with a spherical cavity due to memory-dependent derivative

Abstract

In this article, thermoelastic interaction in a two-temperature generalized thermoelastic unbounded isotropic medium having spherical cavity has been studied in the context of memory-dependent derivative (MDD). The governing coupled equations for the problem associated with kernel function and time delays are considered in the perspective of two-temperature (2 T) three-phase-lag thermoelasticity theory. The bounding surface of the spherical cavity is subjected to mechanical and thermal loading. Using Laplace transform, the problem is transformed from the space–time domain and then solved by the state–space approach method. Suitable numerical technique is used to find the inversion of Laplace transforms. Comparisons are made graphically, between the 2 T three-phase-lag model and 2 T Lord Shulman model with MDD. Also, the effects of time-delay parameter and the kernel function on the distributions of the strain component, thermodynamic temperature, conductive temperature, displacement components, radial and hoop stresses are examined and illustrated graphically. The results show that due to the influence of the three-phase-lag-effect, memory effect, two-temperature parameter, the kernel function and time-delay, all the distributions are affected extensively.