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Magneto-Viscoelastic Materials: Memory Functionals and Rate Equations.

Claudio Giorgi1, Angelo Morro2

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Summary

This study models viscoelastic solids under magnetic fields using two thermodynamic approaches. Objective rate equations offer a simpler, more versatile method for developing magneto-viscoelastic material models.

Keywords:
magneto-viscoelastic materialsmagneto-viscoelasticity of strain rate typememory functionalsrate equationsthermodynamic consistency

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Area of Science:

  • Continuum Mechanics
  • Materials Science
  • Magneto-viscoelasticity

Background:

  • Viscoelastic solids exhibit time-dependent mechanical properties.
  • Magnetic fields introduce complex behaviors in materials.
  • Modeling non-instantaneous responses in materials is challenging.

Purpose of the Study:

  • To develop thermodynamically consistent models for viscoelastic solids under magnetic fields.
  • To compare two distinct modeling approaches: memory functionals and objective rate equations.
  • To explore the potential for creating new magneto-viscoelastic material models.

Main Methods:

  • Utilizing two thermodynamically consistent approaches for modeling.
  • Employing memory functionals dependent on material histories.
  • Applying objective rate equations for a simplified modeling scheme.
  • Deriving a representation formula from the entropy inequality.
  • Using entropy production as a constitutive function.

Main Results:

  • Objective rate equations provide a simpler and more practical modeling framework compared to memory functionals.
  • The simpler scheme facilitates the development of specific models, including magneto-hyperelastic and magneto-hypoelastic materials.
  • The proposed procedure, based on a representation formula and entropy production, offers a novel approach.

Conclusions:

  • Objective rate equations are a more advantageous approach for modeling magneto-viscoelastic solids.
  • The developed methods allow for the creation of diverse magneto-viscoelastic material models.
  • The study advances the understanding and modeling of magnetic field effects on viscoelastic materials.