Modelling of Electro-Viscoelastic Materials through Rate Equations

Area of Science:

• Continuum Mechanics
• Thermodynamics of Materials
• Dielectric Solids

Background:

• Modeling dielectric solids under large deformations requires accounting for complex properties like viscoelasticity and conduction.
• Existing models may lack generality or accuracy in capturing coupled electromechanical and thermal behaviors.

Purpose of the Study:

• To establish general thermodynamic models for dielectric solids undergoing large deformations.
• To incorporate viscoelasticity, electric, and thermal conduction within a unified framework.
• To provide accurate constitutive models for materials like soft ferroelectrics.

Main Methods:

• Utilizing a thermodynamic approach to derive constitutive equations.
• Selecting appropriate fields for polarization and electric fields based on physical principles (angular momentum balance, Euclidean invariance).
• Investigating thermodynamic restrictions using a comprehensive set of variables.

Main Results:

• Developed general models for dielectric solids with viscoelastic properties, electric and thermal conduction.
• Identified suitable fields for polarization and electric fields.
• Demonstrated that few constitutive parameters can accurately fit material behavior, particularly for soft ferroelectrics (e.g., BTS ceramics).
• Incorporated dependence on electric field gradient and entropy production as a constitutive property.

Conclusions:

• The proposed thermodynamic framework provides accurate and general models for large deformation dielectric solids.
• The models offer improved accuracy and generality through explicit representation formulae derived from thermodynamic inequalities.
• This approach is advantageous for material characterization and simulation, especially for advanced dielectric materials.