Homogenized nonlinear constitutive law using Fourier series expansion

This work is concerned with modeling the nonlinear homogonized elastoplastic behavior of a composite comprised of a periodic microstructure under small deformation conditions. A Fourier series approach is used in solving the integral equation [called the periodic Lippmann- Schwingerʹs equation, KrOner, E. (1972) Statistical Continuum Mechanics, p. 110. Springer, Wien] which governs the micr0medu~.uical behavior of the composite material. The nonliavar behavior of fibrous composite is approximated by discretizi .rig the unit cell into subregions in which microplastic strain tensor is assumed to be constant. The method is applied to the case where the individual constituents are elastic-perfectly plastic Von-Mises materials. The elastoplastic homogenized law is used to analyze the behavior of a fibrous boron/aluminum metal-matrix composite under various loading paths. © 1998 Elsevier Science Ltd.