Nonlinear Models of Thermo-Viscoelastic Materials

Area of Science:

• Continuum Mechanics
• Thermodynamics of Materials
• Viscoelasticity and Viscoplasticity

Background:

• Existing models for viscoelastic materials often lack a unified thermodynamic basis.
• Thermodynamic consistency, particularly with the second law, is crucial for developing robust material models.
• The role of entropy production in constitutive modeling requires further exploration.

Purpose of the Study:

• To develop a general thermodynamic scheme for viscoelastic materials.
• To incorporate entropy production as a constitutive function for broader model applicability.
• To establish a framework for nonlinear thermo-viscoelastic and viscoplastic material modeling.

Main Methods:

• Describing constitutive properties using strain, stress, heat flux, and their time derivatives.
• Ensuring constitutive functions are consistent with the second law of thermodynamics.
• Setting the non-negative entropy production equal to a constitutive function.

Main Results:

• A generalized scheme for viscoelastic materials consistent with thermodynamic laws.
• The framework allows for a wider range of constitutive models.
• Special cases include Kelvin-Voigt, Maxwell, Burgers, Oldroyd-B viscoelastic models, and Maxwell-Cattaneo heat conduction.
• The scheme also models viscoplastic materials like Prandtl-Reuss and Bingham-Norton fluids.

Conclusions:

• The proposed thermodynamic scheme provides a unified approach to modeling complex material behaviors.
• Incorporating entropy production as a constitutive function enhances model versatility.
• This framework facilitates the development of advanced nonlinear viscoelastic and viscoplastic models.