Thermoelasticity describes the interaction of the mechanical fields such as stress, strain and displacement with temperature field and investigates the interaction on the basis of the thermodynamics of the irreversible processes. It relates two separate and independently developed sciences: the theory of elasticity and the theory of heat conduction. The two basic branches of elasticity, namely elastostatic and elastodynamics are developed under different thermodynamic assumptions. The problems of static are regarded as isothermal and those of dynamics are said to be adiabatic. Thermoelasticity unifies these two fields. The effect of the temperature field on the strain field is not a one-way phenomenon. The strain field also affects the temperature
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For example, Lord and Shulman (1967) developed a theory of thermoelasticity after including a relaxation time in the Fourier law of heat conduction, whereas Green and Lindsay (1972) developed a theory of thermoelastcity, where two relaxation times are introduced in constitutive equations. Green and Naghdi (1993) proposed a thermoelasticity without energy dissipation. Here, the Fourier’s law is replaced by a heat flux rate-temperature gradient relation. Hetnarski and Ignackzak (1996) introduced a low temperature thermo elasticity. In this model, in comparison to the classical theory, the free energy and the heat flux both depend on the temperature and the strain tensor, and also on the elastic heat flow that satisfies a non-linear evolution equation. Chandrasekharaiah (1998) and Tzou, (1995) formulated a dual phase lag thermoelasticity. They replaced Fourier’s law by an approximation to a modification of Fourier’s law in which two different translation times for the heat flux and the temperature gradient are used. Each of these five models have been developed to eliminate the short comings of the classical dynamical thermo elasticity such as (1) infinite velocities of thermo elastic disturbances, (2) unsatisfactory thermo elastic response of a solid to short heat pulses,(3) poor description of thermo elastic behavior at low temperature (Francis, 1972; Ignaczak, 1981). Out of these five different models of a thermo elastic solid, in which disturbances are transmitted in a wave like manner, only H-I model is strongly non-linear and the rest of the models are
For example, Lord and Shulman (1967) developed a theory of thermoelasticity after including a relaxation time in the Fourier law of heat conduction, whereas Green and Lindsay (1972) developed a theory of thermoelastcity, where two relaxation times are introduced in constitutive equations. Green and Naghdi (1993) proposed a thermoelasticity without energy dissipation. Here, the Fourier’s law is replaced by a heat flux rate-temperature gradient relation. Hetnarski and Ignackzak (1996) introduced a low temperature thermo elasticity. In this model, in comparison to the classical theory, the free energy and the heat flux both depend on the temperature and the strain tensor, and also on the elastic heat flow that satisfies a non-linear evolution equation. Chandrasekharaiah (1998) and Tzou, (1995) formulated a dual phase lag thermoelasticity. They replaced Fourier’s law by an approximation to a modification of Fourier’s law in which two different translation times for the heat flux and the temperature gradient are used. Each of these five models have been developed to eliminate the short comings of the classical dynamical thermo elasticity such as (1) infinite velocities of thermo elastic disturbances, (2) unsatisfactory thermo elastic response of a solid to short heat pulses,(3) poor description of thermo elastic behavior at low temperature (Francis, 1972; Ignaczak, 1981). Out of these five different models of a thermo elastic solid, in which disturbances are transmitted in a wave like manner, only H-I model is strongly non-linear and the rest of the models are