On constitutive equations for thermoelastic dielectric continuum in terms of invariants

• Published in: International journal of engineering science Vol. 49; no. 7; pp. 625 - 634
• Main Author: Usal, Mustafa Reşit
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.07.2011; Elsevier
• Subjects: Analytical and numerical techniques; Asymmetric stress; Balance equations; Constitutive axioms; Constitutive relationships; Dielectric; Dielectrics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat flux; Heat flux vector; Heat transfer; Mathematical analysis; Physics; Polarization; Polarization field; Solid mechanics; Static elasticity (thermoelasticity...); Stresses; Structural and continuum mechanics; Symmetric stress; Thermoelasticity; Vectors (mathematics); Constitutive axioms; Thermoelasticity; Balance equations; Asymmetric stress; Symmetric stress; Dielectric; Heat flux vector; Polarization field; Constitutive equation; Invariant; Constraint; Temperature effect; Heat flow; Potential function; Modeling; Continuum; Thermodynamics; Vector field; Electrodynamics; Stress analysis; Dielectric materials; Thermomechanical properties; Temperature gradient; Asymmetry; Heat transfer
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/j.ijengsci.2011.02.005

Electro-thermomechanical behavior of a thermoelastic dielectric body subject to external loading has been investigated theoretically in the present analysis. The theory is formulated in the context of continuum electrodynamics. The reaction of the body subject to external loads is expressed in symmetric stress, electrical polarization and heat flux. The solid medium is assumed to be linear, dielectric, isotropic, incompressible and dependent on temperature gradient. It has been observed that, as a result of thermodynamic constraints, the stress potential function is dependent on the deformation tensor, the electric field vector and the temperature, while the heat flux vector function is dependent on the deformation tensor, the electric field vector, the temperature and temperature gradient. To determine arguments of the stress potential and the heat flux vector functionals, findings of the theory of invariants have been used as a method because of that isotropy constraint is imposed on the material. As a result, constitutive equations of symmetric stress, polarization field and heat flux vector have been obtained in both material and spatial coordinates and asymmetric stress has been found using the expressions of symmetric stress and polarization field.