A finite element modeling for anisotropic dielectric elastomer energy harvesters with inhomogeneous displacement fields

Abstract

In this paper, we are to investigate the effects of imparting anisotropy to dielectric elastomers (DEs) to evaluate the promising capabilities of this phenomenon in energy harvesting (EH) enhancement. To this end, we employ the principle of virtual work to obtain the governing equations and the boundary conditions of dielectric elastomers at finite strains. As for the material law, it incorporates three parts, including an isotropic, an anisotropic, and an electric one with no modes of dissipation. Having to deal with inhomogeneous displacement fields necessitates the employment of finite element (FE) simulations. Moreover, a staggered algorithm has been put into use which is capable of reducing computational expense while producing the same results as that of a fully coupled solution. Further, F-bar method has been selected to alleviate the issue of volumetric locking. The aforementioned finite element implementation is conducted through a computer program. It is noteworthy that all the terms involved in FE modeling, particularly electroelastic moduli and the terms originated from the follower load assumption are fully derived. Three energy harvesting applications, including a cylindrical tube, a diaphragm, and an annular membrane which satisfy the axisymmetric assumptions, are investigated. In the interest of verifying the developed axisymmetric element, the finite element results have been compared with that of analytical ones for a one-dimensional homogenous actuation problem. Intended to reveal the efficacy of imparting anisotropy to DEs in EH, we fix all the other contributing factors in the energy harvesting cycle for each application. As a result, corresponding isotropic and anisotropic cases become possible whose only difference is in the existence or absence of anisotropic fibers. Eventually, through numerical simulations it is proved that imparting anisotropy to dielectric elastomers in most cases culminates in favor of energy harvesting. Particularly, the maximum amount of relative energy harvesting difference of corresponding isotropic and anisotropic cases for the cylindrical tube, the diaphragm, and the annular membrane is achieved to be 27.75%, 10.61%, and 19.76%, respectively, in favor of the anisotropic cases.