Determination of constitutive equations dependent on temperature changes for dielectric materials having micro-voids

Abstract

A damage constitutive model based on continuum damage mechanics (CDM) is proposed to investigate the electro-thermomechanical behavior of a thermoelastic dielectric structure in the present paper. The solid medium is assumed to be dielectric, incompressible, homogeneous, dependent on temperature gradient, having micro-voids, and showing linear elastic behavior. The matrix material made of elastic material involving an artificial anisotropy due to the existence of micro-voids has been assumed as an isotropic medium. Damage is incorporated by two symmetric, second-rank, tensor-valued, internal state variables which represent the total areas of “active” and “passive” voids contained within a representative volume element. Using fundamental concepts of continuum electrodynamics, CDMs and irreversible thermodynamics, the constitutive functionals have been obtained. It has been detected as a result of the thermodynamic constraints that stress potential function depends on two symmetric tensors and a vector, whereas the heat flux vector function depends on two symmetric tensors and two vectors. Since the matrix material has been assumed as an isotropic medium, the constitutive equations based on the constitutive functionals, which are stress potential and heat flux vector, have been obtained using the theory of invariants. Finally, the constitutive equations belonging to symmetric stress, polarization field, asymmetric stress, heat flux vector, and strain energy density release rate have been written in terms of material coordinate description.

Keywords:

• Damage
• thermoelasticity
• dielectric
• invariants
• constitutive equations

Acknowledgments

The authors express their thanks to the anonymous referee(s) who kindly provided the suggestions and comments to improve the quality of the paper. The authors are also grateful to the editor Professor Pankaj Kumar Choudhury for his editorial helping.

Disclosure statement

No potential conflict of interest was reported by the authors.