Duc Khoi Vu

Material and Spatial Motion Problems in Nonlinear Electro- and Magneto-elastostatics

In this paper, material and spatial motion problems of the coupled nonlinear problem of electro-and magneto-elastostatics are discussed in the context of non-potential loading where mechanical loads are not assumed to be derived explicitly from some potential. A virtual work approach is used to derive the corresponding balance equations and boundary conditions of the material motion problems.

On rate-dependent dissipation effects in electro-elasticity

Abstract This paper deals with the mathematical modelling of large strain electro-viscoelastic deformations in electro-active polymers. Energy dissipation is assumed to occur due to mechanical viscoelasticity of the polymer as well as due to time-dependent effective polarisation of the material. Additive decomposition of the electric field E = E e + E v and multiplicative decomposition of the deformation gradient F = F e F v are proposed to model the internal dissipation mechanisms. The theory is illustrated with some numerical examples in the end.

On the spatial and material motion problems in nonlinear electro-elastostatics with consideration of free space

In this work the formulation of spatial and material motion problems in nonlinear electro-elastostatics is considered using an energy approach, which takes into account the contribution of the free space surrounding a nonlinearly polarized body undergoing large deformation. The free space can have a huge impact on the electric field and on the deformation field inside a body made of materials with low electric permittivity such as the so-called electronic electroactive polymers (EEAPs). The contribution of the free space can be taken into account by using the electric flux and the Maxwells traction acting on the boundary of the body. These two quantities can be expressed in terms of a stored energy density function. By using a stored energy density function for both the material body and the (finite or infinite) free space, the governing equations of both spatial and material motion problems are derived by considering the change of energy with respect to a change in the spatial or material configuration. In the spatial motion problem, well-known definitions for electric and mechanical quantities are derived. In the material motion problem, in addition to the derivation of configurational forces, this approach reveals the formulas for the part of energy that is released from the system material body, applied forces in response to a change in the material configuration, which are particularly useful in the study of defects such as crack propagation. The same approach can be used in the case of nonlinear electro-thermo-mechanical coupling and constitutes the direction for future works.

The Concept of Material Forces in Nonlinear Electro-elastostatics

In this work we review the application of material forces in electro-elastostatics, especially in the computation of the so-called vectorial J-integral in crack problems. The formulations of material forces take into account the contribution of the outer space surrounding the body under consideration. It is shown that the contribution of the outer space is of importance when the polarization is relatively weak, for example in the case of electronic electro-active polymers, and that this contribution can be ignored if the polarization is much higher than that of the surrounding space like in most piezoelectric materials.