Investigation of Uniqueness, Reciprocity Theorems and Deformation in Multi-Phase-Lags Anisotropic Thermoviscoelastic Diffusion Model

A new model involving the equations of thermoviscoelastic diffusion under multi-phase-lags for anisotropic medium (ATDM) is presented. The simulated model is obtained after modifying the basic Fourier’s [1] and Fick’s [2] laws to involve the higher order time derivatives of heat flow vector, the gradient of temperature, diffusing mass flux, and chemical potential gradient. The governing equations for the ATDM are considered to establish uniqueness and reciprocity theorems. By applying the Laplace transform a uniqueness theorem for the considered model is proved and the reciprocity theorem is derived. Instantaneous concentrated body forces, heat sources, and chemical potential sources along with moving heat and chemical potential sources are taken to illustrate the applications of the reciprocity theorem for a specific case. It has been recognized that these theorems are impacted by the perceptivity of the involved field variable along with the variations of parameters involving higher-order time derivatives. Also, the orthotropic thermoviscoelastic diffusion with a multi-phase-lags model for the one-dimensional case presents a deformation due to thermal and chemical potential sources. As the application of the problem instantaneous thermal and instantaneous chemical potential sources are taken. Comparison has been made for Lord-Shulman (LS), dual phase lags, and higher order time derivatives on displacement, stress, temperature, and chemical potential. Some unique cases are also established and correlated with known results. The effect of phase-lags plays an important role in processing and characterization to improve material properties and find applications in geomechanics, earthquake engineering, and the designing of new materials.