Nonlinear viscoelasticity of strain rate type: an overview

Area of Science:

• Material Science
• Solid Mechanics
• Nonlinear Dynamics

Background:

• Many natural materials exhibit non-elastic deformations, characteristic of viscoelastic solids.
• Viscoelastic materials have widespread applications in engineering, material science, and medicine.
• Accurate prediction of mechanical behavior requires understanding strain rate sensitivity.

Purpose of the Study:

• To model the nonlinear response of viscoelastic solids.
• To focus on nonlinear viscoelasticity of the strain rate type.
• To develop a constitutive relation for stress dependent on strain and strain rate.

Main Methods:

• Introduction to basic terminology: kinematics, material frame-indifference, and thermodynamics.
• Derivation of the most general model for nonlinear viscoelasticity of strain rate type.
• Analysis of governing equations and constitutive relationships.

Main Results:

• A general model for nonlinear viscoelasticity of strain rate type was obtained.
• The long-term behavior of solutions was discussed.
• The study provides a framework for predicting mechanical behavior based on strain rate sensitivity.

Conclusions:

• The developed model is mathematically tractable and experimentally relevant.
• Knowledge of strain rate sensitivity is crucial for accurate mechanical predictions.
• The model has potential applications in various scientific and engineering fields.