A nonlinear spectral rate-dependent constitutive equation for electro-viscoelastic solids
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Zeitschrift f¨ ur angewandte Mathematik und Physik ZAMP
A nonlinear spectral rate-dependent constitutive equation for electro-viscoelastic solids M. H. B. M. Shariff , R. Bustamante and J. Merodio Abstract. In this communication a spectral constitutive equation for nonlinear viscoelastic-electroactive bodies with shortterm memory response is developed, using the total stress formulation and the electric field as the electric independent variable. Spectral invariants, each one with a clear physical meaning and hence attractive for use in experiment, are used in the constitutive equation. A specific form for constitutive equation containing single-variable functions is presented, which are easy to analyze compared to multivariable functions. The effects of viscosity and an electric field are studied via the results of boundary value problems for cases considering homogeneous distributions for the strains and the electric field, and some these results are compared with experimental data. Mathematics Subject Classification. 74F99, 74D10. Keywords. Nonlinear electro-viscoelasticity, Spectral physical invariants, Deformation indicators, Rate of deformation indicators.
1. Introduction In the last 2 decades there has been a renewed interest in the study of electromagnetic interactions with solid media (see, for example, [23] and the references therein). In the particular case of electric interactions, the interest comes mostly from the development of some composite materials, where electro (or magneto) active particles are added to a rubber-like matrix during curing [4,12]. In other cases thin plates made of rubber are coated with electrodes, which upon the application of an electric potential, are compressed due to the electric forces that appear between the electrodes [3]. In biomechanics some types of soft tissues such as muscles can react to electric fields (see [7] and the references mentioned therein). We note that most of the early mechanical models of electro-active materials are simplified by assuming that these materials are elastic, i.e., there is no dissipation of energy [10,11,23]. However, in reality, most materials are not purely elastic and they exhibit some form of dissipation. In view of this, we are particularly concerned with viscoelastic-electroactive bodies that represent a wide range of materials and physical systems sensitive to mechanical forces and electric fields. Applications where these materials are used, for example, include biomimetics, micro-robotics and actuators. This has created considerable interest during the last years and many publications have resulted from attempts to understand the influence of electric fields on the mechanical behaviour of viscoelastic solids (see, for example, [1,2,13,16,17]). For example, in reference [8], Chen proposed a very general model for electro-thermo-viscoelastic solids with memory, using a Gibbs’ potential. In references [5,9,19,43,44] models have been presented based on the decomposition of the energy into an electro-elastic part plus a visco-electro-elastic
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