Micro-Mechanical Model of a Composite Containing a Conservative Nonlinear Electro-Magneto-Thermo-Mechanical Material

In this paper, we present an elasticity formulation using a concentric cylinders assemblage to investigate the response of a composite system containing a conservative nonlinear electro-magneto-thermo-mechanical (EMTM) material. The nonlinearity in the EMTM material is mathematically represented in the constitutive relations with terms coupling strain, electric/magnetic fields, temperature, and stress. These relations are representative of piezoelectric, electrostrictive, and magnetostrictive materials. The electric-magnetic-thermal field inside the composite material is assumed to be invariant with respect to position; this permits a closed form solution to be presented. The analytical model provides point wise stresses and strains in each constituent and is useful for evaluating possible locations for damage initiation and effective properties for the coupled material system. Parametric studies are presented to investigate the influence of constituents and actuator geometry on the material system's effective properties. Analytical results generated for a Terfenol-D composite indicate that nonlinear terms must be included to accurately characterize its response to large changes in stress or magnetic field strengths.