Abstract
Electroelastic materials, as for example, 3M VHB 4910, are attracting attention as actuators or generators in some developments and applications. This is due to their capacity of being deformed when submitted to an electric field. Some models of their actuation are available, but recently, viscoelastic models have been proposed to give an account of the dissipative behaviour of these materials. Their response to an external mechanical or electrical force field implies a relaxation process towards a new state of thermodynamic equilibrium, which can be described by a relaxation time. However, it is well known that viscoelastic and dielectric materials, as for example, polymers, exhibit a distribution of relaxation times instead of a single relaxation time. In the present approach, a continuous distribution of relaxation times is proposed via the introduction of fractional derivatives of the stress and strain, which gives a better account of the material behaviour. The application of fractional derivatives is described and a comparison with former results is made. Then, a double generalisation is carried out: the first one is referred to the viscoelastic or dielectric models and is addressed to obtain a nonsymmetric spectrum of relaxation times, and the second one is the adoption of the more realistic Mooney–Rivlin equation for the stress–strain relationship of the elastomeric material. A modified Mooney–Rivlin model for the free energy density of a hyperelastic material, VHB 4910 has been used based on experimental results of previous authors. This last proposal ensures the appearance of the bifurcation phenomena which is analysed for equibiaxial dead loads; time-dependent bifurcation phenomena are predicted by the extended Mooney–Rivlin equations.
Highlights
Viscoelastic models have been proposed to give an account of the dissipative behaviour of the electroelastic materials [1,2,3,4,5,6,7,8,9,10,11,12]
A first-order kinetic, which is represented by a first-order differential equation, is equivalent to considering a single relaxation time associated with the relaxation process
As the differential fractional algebraic equations (DFAE) given by (21a,b) do not have a closed solution, we approximate its solution by using a numerical method combining the fractional forward Euler method, for fractional differential equations applied to Equation
Summary
Viscoelastic models have been proposed to give an account of the dissipative behaviour of the electroelastic materials [1,2,3,4,5,6,7,8,9,10,11,12]. In the theoretical background, a substantial modification of the classical model equations for the purely electroelastic materials is necessary in order to consider the viscoelastic and dielectric relaxation effects both of which are intrinsically dissipative. In this sense, an approach based on classical irreversible thermodynamics has been proposed by Suo et al [4]. Attention is paid to enlarge the viscoelastic and dielectric effects in electroelastic materials to consider the case of a distribution of relaxation times For this purpose, the simplified approach used in Ref.
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