Abstract
Exact solutions for nonlinear composites undergoing finite deformation are in general difficult to find. In this article, such a solution is obtained for a two-phase composite reinforced with elliptic fibers under anti-plane shear. The analysis is based on the theory of hyperelasticity with both phases characterized by incompressible neo-Hookean strain energies, and is carried out when the composite elliptic cylinder assemblage carries a confocal microgeometry. The problem for a class of compressible neo-Hookean materials is also studied. The analytical results for the stress and strain distributions are verified with finite element calculations where excellent agreement is found. We then derived the explicit relations for the macroscopic nominal stress tensor and the effective secant axial-shear moduli under finite deformation. To make contact with existing micromechanics theories, it is further demonstrated that, within the small-strain framework, the obtained axial-shear moduli with conformal arrangement coincide with those of the double-inclusion model [Hori, M., Nemat-Nasser, S., 1993. Double-inclusion model and overall moduli of multi-phase composites. Mech. Mater. 14, 189–206].
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