A mathematical model for three-phase-lag dipolar thermoelastic bodies.

Area of Science:

• Continuum Mechanics
• Thermodynamics
• Solid Mechanics

Background:

• Thermoelasticity describes material response to thermal and mechanical stimuli.
• Dipolar thermoelasticity incorporates higher-order gradient effects.
• Three-phase-lag models capture complex relaxation phenomena in heat conduction and stress propagation.

Purpose of the Study:

• To model a mixed initial-boundary value problem for a three-phase-lag dipolar thermoelastic body.
• To establish fundamental theoretical results for this complex material model.
• To generalize existing variational principles in elasticity.

Main Methods:

• Formulation of a mixed initial-boundary value problem.
• Application of constitutive laws specific to three-phase-lag dipolar thermoelasticity.
• Mathematical analysis to derive uniqueness and reciprocal theorems.

Main Results:

• A uniqueness result for the considered initial-boundary value problem.
• Proof of a reciprocal theorem for the thermoelastic system.
• Derivation of a variational principle generalizing Gurtin's principle.

Conclusions:

• The study provides a rigorous mathematical framework for three-phase-lag dipolar thermoelasticity.
• The established uniqueness and reciprocal theorems are crucial for numerical simulations and theoretical analysis.
• The generalized variational principle offers a powerful tool for further research in advanced elasticity.