Abstract
This work is concerned with modeling the nonlinear mechanical deformation of composites comprised of a periodic microstructure under small displacement conditions at elevated temperatures. The practical motivation for such work stems from the need to design and optimize new multiphase materials and to predict their micromechanical and bulk material behavior under in-service thermomechanical loading conditions.
Two different methods, one based on a Fourier series approach and the other on a Green’s function approach, are used in modeling the micromechanical behavior of the composite material. These two methods are shown to be equivalent to each other via the Poisson sum formula. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall “effective” constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element structural analysis programs.
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Walker, K.P., Jordan, E.H., Freed, A.D. (1990). Equivalence of Green’s Function and the Fourier Series Representation of Composites with Periodic Microstructure. In: Weng, G.J., Taya, M., Abé, H. (eds) Micromechanics and Inhomogeneity. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8919-4_33
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DOI: https://doi.org/10.1007/978-1-4613-8919-4_33
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