Thermomechanical constraints and constitutive formulations in thermoelasticity

Abstract

We investigate three classes of constraints in a thermoelastic body: (i) a deformationtemperature constraint, (ii) a deformation-entropy constraint, and (iii) a deformationenergy constraint. These constraints are obtained as limits of unconstrained thermoelastic materials and we show that constraints (ii) and (iii) are equivalent. By using a limiting procedure, we show that for the constraint (i), the entropy plays the role of a Lagrange multiplier while for (ii) and (iii), the absolute temperature plays the role of Lagrange multiplier. We further demonstrate that the governing equations for materials subject to constraint (i) are identical to those of an unconstrained material whose internal energy is an affine function of the entropy, while those for materials subject to constraints (ii) and (iii) are identical to those of an unstrained material whose Helmholtz potential is affine in the absolute temperature. Finally, we model the thermoelastic response of a peroxidecured vulcanizate of natural rubber and show that imposing the constraint in which the volume change depends only on the internal energy leads to very good predictions (compared to experimental results) of the stress and temperature response under isothermal and isentropic conditions.

Efficient Simulation of Nonlinear Heat Transfer during Thermal Spraying of Complex Workpieces

“…Furthermore, the developed framework shall be used to extend the optimisation software described in [26] in order to be able to optimise temperature quantities. Another aspect of future research is the extension towards a thermo-mechanically coupled framework, [27], which will enable the analysis of residual stresses and damage due to thermal spraying as discussed in, e.g., [28] [29].…”

Theoretical investigation on polar dielectric with large electrocaloric effect as cooling devices

“…[10][11][12][13] As the temperature rises, internal energy QðTÞ ¼ c 0 ðT À T 0 Þ. According to the relation of specific heat for constant volume and entropy, c 0 ¼ T @S @T , we obtain S ¼ c 0 ln T T 0 , where c 0 is the specific heat of polar dielectric, T 0 and T are the temperatures in reference and current states, respectively.…”