On the Influence of the Coupled Invariant in Thermo-Electro-Elasticity

A complete thermo-electro-viscoelastic characterization of dielectric elastomers, Part II: Continuum modeling approach

“…In these definitions, the viscous shear moduli µ v i and the relaxation times τ i have been introduced. In accordance with our previous works [45,46], we select three internal variables. Thus, three pairs of shear moduli and relaxation times have to be identified using the results of the cyclic loading tests conducted at room temperature.…”

“…This framework will be derived step by step, beginning with the isothermal case. The information presented therein has been investigated as well in our previous publication [45] where, in addition to mathematical formulations, a number of illustrative boundary value problems were presented. Subsequently, a thermodynamically consistent formulation for a thermally coupled energy function is derived.…”

“…In the context of this work, we will restrict ourselves to the initial formulation based directly on the right Cauchy-Green tensor. The interested reader is referred to [45] for a more detailed insight into the differences between the two formulations. It should be noted however that, even though the selection of an energy function that contains the coupling invariants I 5 or I 6 in general results in a connection between the electric field and the mechanical response, it does not necessarily mean that it correctly replicates the behavior of a dielectric elastomer under the loading of an electric field.…”

A nonlinear thermomechanical formulation for anisotropic volume and surface continua

“… 5. The multiplicative decomposition can be used to decompose the deformation into thermal, electrical, magnetic, and mechanical parts see Mehnert et al [168] and Ethiraj and Miehe [169]. …”