The Elastic Dielectric

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

“…Note that the small deformation assumption is prevalent throughout the phase field modeling literature. The analysis of large deformations would introduce the concept of Maxwell stresses (Toupin, 1956;McMeeking and Landis, 2005), which are assumed to be higher order effects that can be neglected. Following previous phase field modeling approaches, the effects of large deformations will not be considered here, but their incorporation within the theory is possible.…”

Implicit constitutive relations for nonlinear magnetoelastic bodies

“…expressions similar to (3.1). The use of such an energy function (depending only on the deformation gradient and the magnetization) was also suggested on a study on nonlinear dielectrics by Toupin [78], as was acknowledged by Brown (see Preface of [31] and the third paragraph in pp. 995 of [31]).…”

“…Early systematic treatments of the mathematical modelling of magnetoelastic materials can be found in the works by Voigt [67,68], the papers by Volterra [69] and by Mason [73]. Many of these works have been influenced by the different theories on electroelasticity, which were developed earlier (see [78] and the review in §3(a) in [4]). In all these works as well as several others that we will cite later, the main assumption has been to express the stress tensor (either the total stress tensor or other definitions for it [37,38,58] in the case of bodies with memory) of the strains, 4 i.e.…”

Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries

“…The local form of the Maxwell equations are given by Here, ρ is the mass density, σ is the total stress [10,11] generated owing to combined magnetomechanical effect, f b is the non-magnetic body force density. The local form of the energy balance …”