Nonuniform transformation field analysis based reduced-order model of high-fidelity generalized method of cells

The accurate prediction of a composite's nonlinear behavior using multiscale modeling techniques relies heavily on the description of microscale features and requires many internal variables, leading to high computational costs. This paper presents a reduced-order model (ROM) for composite materials based on a novel adaptation of nonuniform transformation field analysis (NTFA) in conjunction with the high-fidelity generalized method of cells (HFGMC) micromechanics theory accounting for micro constituent damage. First, the composite's nonlinear behavior is simulated using the HFGMC technique with constituent damage represented as damage-induced inelastic strains. The nonuniformity in the inelastic strains is then approximated using a set of tensorial deformation modes. Next, a macroscopic continuum damage model is formulated based on the inelastic modes to have the same evolution function as their microscopic counterpart. The NTFA procedure is applied in a three-dimensional setting, followed by a detailed description of the localization operators necessary for linearizing the homogenized constitutive equations. Last, the ROM's capability to capture damage effects using only a finite set of internal variables is demonstrated by comparing the predicted global and local responses through HFGMC simulations for different loading paths. The presented model is shown to decrease the computational cost of micromechanics-based unit cell homogenization significantly.