Abstract
A mathematical model of two temperature thermo-visco-elasticity has been constructed in the circumstances of a new thought of heat conduction with memory-dependent derivative (MDD) in a piezoelastic body occupying the positive half of real axis with stress less boundary and heat output. The three-phase-lag thermoelastic model (TPL), Lord-Shulman model (LS) and dual-phase lag (DPL) model are combined into a unified formulation. In the Laplace-transform domain Vector-matrix method have been applied to write the basic equations which is then worked out by the state-space technique. Fourier-series expansion techniques have been applied to discover the numerical transposition of the transform. The results for stress distribution, strain distribution and conductive temperature have been worked out numerically and presented pictorially. The aftereffect of the MDD on the results has been investigated. According to this new mathematical model of thermo-visco-elasticity, we can arrange the materials according to an advanced parameter.
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