Fully-coupled electro-magneto-elastic behavior of unidirectional multiphased composites via finite-volume homogenization

Abstract

The effective and localized electro-magneto-elastic behavior of periodic unidirectional composites is investigated in this work. Instead of adopting the classical micromechanics models or variational principle-based finite-element (FE) techniques, the finite-volume direct averaging micromechanics (FVDAM) is extended to fulfill this task by incorporating fully-coupled electro-magneto-elastic constitutive relations. Consistent with the mathematical homogenization theories, the mechanical displacements and electric/magnetic potentials are partitioned using two-scale expansion involving the macroscopic and fluctuating contributions. The generalized local stiffness matrices are constructed explicitly by relating the surface-averaged tractions, electric displacements, and magnetic inductions to the surface-averaged mechanical displacements and electric/magnetic potentials, followed which the continuity and periodic boundary conditions are applied. The homogenized coefficients and localized stress, electric/magnetic field distributions are validated extensively against the exact generalized Eshelby solution and an in-house FE program, as well as the experimental measurements, where perfect agreements are observed for all cases. The efficiency and convergence of the proposed multiphysics FVDAM (MFVDAM) are tested by comparing the execution time and localized fields as a function of mesh discretization, with the multiphysics FE (MFEM) results as references. Besides, the MFVDAM is encapsulated into the particle swarm optimization algorithm to deduce the optimal fiber volume fraction at which maximum magnetoelectric coupling effect may occur in the composite system with piezomagnetic ceramics reinforced with piezoelectric unidirectional fibers.