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A multiscale (micro-to-macro) analysis is proposed for the prediction of the finite strain behavior of composites with hyperelastic constituents and embedded localized damage. The composites are assumed to possess periodic microstructure and be subjected to a remote field. At the microscale, finite-strain micromechanical analysis based on the homogenization technique for the (intact) composite is employed for the prediction of the effective deformation. At the macroscale, a procedure, based on the representative cell method and the associated higher-order theory, is developed for the determination of the elastic field in the damaged composite. The periodic composite is discretized into identical cells and then reduced to the problem of a single cell by application of the discrete Fourier transform. The resulting governing equations, interfacial and boundary conditions in the Fourier transform domain, are solved by employing the higher-order theory in conjunction with an iterative procedure to treat the effects of damage and material nonlinearity. The initial conditions for the iterative solution are obtained using the weakly-nonlinear material limit and a natural fixed-point iteration. A locally-convergent low-memory Quasi-Newton solver is then employed. A new algorithm for the implementation of the solver is proposed, which allows storing in the memory directly the vector-function history-sequence, which may be advantageous for convergence-control based on specific components of the objective vector-function. The strong-form Fourier transform-based approach employed here, in conjunction with the new solver, enables to extend the application of the method to nonlinear materials and may have computational efficiency comparable or possibly advantageous to that of standard approaches., Comment: 38 pages, 28 figures

An analytical procedure, which couples electric, magnetic, thermal and mechanical effects is presented for the prediction of the response of unidirectional fiber-reinforced composites that are subjected to electric field, applied in the fibers' direction. It is assumed that at least one of the phases of the composite (e.g., the fibers) is electrically conductive, and that all phases are thermally conductive. The composite is assumed to occupy a finite, symmetric domain which is discretized into a double array of subcells. The governing equations, with the interfacial and boundary conditions, are satisfied in the integral sense. The externally applied field generates electric current, which induces a magnetic field as well as temperature increase. The mechanical deformation of the composite results from the combined effect of the ponderomotive force, which is created by the magnetic field, and the temperature distribution within the constituents. The purpose of the present paper is three-fold. (a) To perform quantitative analysis of the model for the ponderoromotive force in deformable media. (b) To present computational strong-form treatment of the magneto-mechanical boundary-value problem in a composite. (c) To suggest a computational apparatus for deriving the response of a sensor/actuator excited by an applied electric field or electric field gradient. Application is given, presenting the magnetic, thermal and mechanical field distributions, as well as the macroscopic (global) response of a composite, which consists, for simplicity, of two iron fibers embedded in an epoxy matrix., Comment: 32 pages, 18 figures

The high-fidelity generalized method of cells micromechanics theory has been extended for the prediction of the effective property tensor and the corresponding local field distributions for composites whose constituents are governed by vector constitutive laws. As shown, the shear analogy, which can predict effective transverse properties, is not valid in the general three-dimensional case. Consequently, a general derivation is presented that is applicable to both continuously and discontinuously reinforced composites with arbitrary vector constitutive laws and periodic microstructures. Results are given for thermal and electric problems, effective properties and local field distributions, ordered and random microstructures, as well as complex geometries including woven composites. Comparisons of the theory's predictions are made to test data, numerical analysis, and classical expressions from the literature. Further, classical methods cannot provide the local field distributions in the composite, and it is demonstrated that, as the percolation threshold is approached, their predictions are increasingly unreliable. XXXX It has been observed that the bonding between the fibers and matrix in composite materials can be imperfect. In the context of thermal conductivity, such imperfect interfaces have been investigated in micromechanical models by Dunn and Taya (1993), Duan and Karihaloo (2007), Nan et al. (1997) and Hashin (2001). The present HFGMC micromechanical method, derived for perfectly bonded composite materials governed by vector constitutive laws, can be easily generalized to include the effects of weak bonding between the constituents. Such generalizations, in the context of the mechanical micromechanics problem, involve introduction of a traction-separation law at the fiber/matrix interface and have been presented by Aboudi (1987), Bednarcyk and Arnold (2002), Bednarcyk et al. (2004) and Aboudi et al. (2013) and will be addressed in the future.