Modeling memory-dependent derivative on photothermoelastic half space in the presence of non-local and hyperbolic two temperatures

The purpose of this paper is developed a new model of photothermoelastic with memory-dependent derivatives (PMDD) under non-local (NL) parameter, dual phase lag (DPL) and hyperbolic two temperature (HTT). The governing coupled equations of the considered model with time delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to a two-dimensional problem of a half-space. Integral transform involving Laplace and Fourier transforms reduced the governing equations into ordinary differential equation. The arbitrary constants in the solution are determined by considering the loading environment on the surface. Three different categories of the sources are taken to explore the application as (i) normal force (ii) thermal source (iii) carrier density source. In the new domain, the closed form expressions of physical quantities like displacement, normal stress, conductive temperature field and carrier density distribution are derived. The numerical inversion method is employed to recover the results in a physical domain. The impact of non-local parameter, dual phase lag and hyperbolic two-temperature with and without MDD (memory dependent derivative) along with variations of all kernel functions on physical field variables are presented in form of graphs. Unique cases are also explored. The problem assumes great significance in an earthquake region when we think of variation of particle motion as a possible precursor for earthquake prediction. The results obtained are also helpful in designing the semiconductor materials in the course of coupled elastic, thermal, plasma waves and also find the application in the material and engineering sciences.