The variational asymptotic method for unit cell homogenization (VAMUCH) is a unified micromechanical numerical method that is able to predict the effective properties of heterogeneous materials and to recover the microscopic stress/strain field. The objective of this paper is to incorporate elastoplastic material behaviors into the VAMUCH to predict the nonlinear macroscopic/microscopic response of elastoplastic heterogeneous materials. The constituents are assumed to exhibit various behaviors including elastic/plastic anisotropy, isotropic/kinematic hardening, and plastic non-normality. The constitutive relations for the constituents are derived and implemented into the theory of VAMUCH. This theory is implemented using the finite element method, and an engineering code, VAMUCH, is developed for the micromechanical analysiso of unit cells. The applicability, power, and accuracy of the theory and code of VAMUCH are validated using several examples including predicting the initial and subsequent yield surfaces, stress-strain curves, and stress-strain hysteresis loops of fiber reinforced composites. The VAMUCH code is also ready to be implemented into many more sophisticated user-defined material models.

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