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Studying Large Amplitude Oscillatory Shear Response of Soft Materials

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Mathematical and numerical model for nonlinear viscoplasticity.

N Favrie¹, S Gavrilyuk

¹Université d'Aix-Marseille and C.N.R.S. U.M.R. 6595, IUSTI, Project SMASH, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|June 22, 2011

Summary

This study introduces a new macroscopic model for elastic-plastic solids, incorporating separable internal specific energy. The model accurately describes material behavior, including relaxation and stress decay during plastic deformation.

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Area of Science:

Solid Mechanics
Materials Science
Continuum Mechanics

Background:

Elastic-plastic solids exhibit complex behaviors under stress.
Existing models may not fully capture phenomena like stress relaxation during plastic deformation.

Purpose of the Study:

To derive a macroscopic model for elastic-plastic solids.
To incorporate separable internal specific energy into the model.
To ensure compatibility with established yield criteria and material behaviors.

Main Methods:

Derivation of a macroscopic model based on separable internal specific energy.
Decomposition of internal specific energy into hydrodynamic and shear parts.
Construction of relaxation terms compatible with the von Mises yield criterion.

Main Results:

A novel macroscopic model for elastic-plastic solids is presented.
The model includes separable internal specific energy (hydrodynamic and shear components).
Maxwell-type material behavior is demonstrated, showing stress tensor decay during plastic deformation.

Conclusions:

The developed model effectively describes elastic-plastic solids.
It accurately captures relaxation phenomena and stress decay.
Numerical examples validate its ability to represent real physical phenomena.