Finite-Strain Homogenization Models for Anisotropic Dielectric Elastomer Composites
This chapter is concerned with a homogenization framework for electroelastic composite materials at finite strains. The framework is used to develop constitutive models for dielectric elastomer composites consisting of initially aligned, rigid dielectric inclusions that are distributed randomly in a dielectric elastomeric matrix. A strategy is proposed to partially decouple the mechanical and electrostatic effects in the composite by writing the effective electroelastic energy of the composite in terms of a purely mechanical energy term together with a purely electrostatic energy term that are linked only by the unknown particle rotations. In addition to the macroscopic constitutive relation for the composite, estimates are also generated for the evolution of the average particle orientation as a function of the applied mechanical and electric fields. The resulting estimates account for the electric torques and dipolar forces on the particles that are generated as a consequence of externally applied electric fields.
This work was begun with the support of the Applied Computational Analysis Program of the Office of Naval Research under Grant N000141110708 and completed with the support of the Applied Math Program of the National Science Foundation under Grant No. DMS-1613926.
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