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A theory is developed for evaluation of nonlinear elastic moduli of compositematerials with nonlinear inclusions dispersed in another nonlinear material(matrix). We elaborate a method aimed for determination of elastic parametersof a composite: its linear elastic moduli (second-order elastic constants) andnonlinear elastic moduli, which are known as the Murnaghan moduli (third-orderelastic constants). We find an analytical form for the effective Murnaghanmoduli of a composite with spherical inclusions. The effective moduli dependlinearly on Murnaghan moduli of constituents. The results obtained have beenverified through numerical modeling using the finite element method.

Nonlinear elastic moduli of composite materials with nonlinear spherical inclusions dispersed in a nonlinear matrix