Magneto-Viscoelastic Materials: Memory Functionals and Rate Equations

Abstract

The properties of viscoelastic solids subject to a magnetic field are modelled within two thermodynamically consistent approaches that are typical of models with a non-instantaneous response. One is based on memory functionals: the reversible changes are described by the instantaneous response, while the dissipativity is expressed by the dependence on histories. The other approach involves objective rate equations. While memory functionals lead to the difficulty of determining thermodynamically consistent free energy functionals, rate equations result in a simpler scheme. The greater simplicity allows the discovery of, in particular, models of magneto-hyperelastic materials, magneto-hypoelastic materials, and various forms of magneto-viscoelastic behaviour. The novelty of the procedure is based on two features: a representation formula, originating from the entropy inequality, and the use of the entropy production as a constitutive function. Relations with other approaches in the literature are examined in detail.

Modeling of heat conduction through rate equations

“…Secondly, the entropy production is viewed as given by a constitutive function as was suggested in [20] and developed e.g. in [21][22][23]. This allows a wider set of admissible thermodynamic processes.…”

Modelling of Electro-Viscoelastic Materials through Rate Equations

“…To establish a thermodynamically consistent scheme for dielectrics undergoing large strains, we follow some ideas that have lately been applied to hysteretic phenomena [ 7 , 8 , 9 ]. First, the entropy production is viewed as a constitutive property which has to be determined using a constitutive equation in accordance with the second-law inequality (see the systematic procedure developed in [ 10 ]).…”