Data Driven TFA-based Homogenization of Nonlinear Composites
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The increasing adoption of advanced composite materials in engineering applications requires efficient tools for predicting their nonlinear mechanical response while accounting for material heterogeneities. Accurate yet computationally affordable predictions are particularly critical for nonlinear composites, where the number of internal variables and the associated computational cost may become prohibitive. A common approach to investigate the overall mechanical behavior of such materials relies on micromechanical homogenization techniques applied on a Representative Volume Element (RVE). Among the available homogenization methods for nonlinear materials, Transformation Field Analysis (TFA), originally proposed by Dvorak [1], represents an efficient strategy to evaluate the RVE response while accounting for nonlinear phenomena. Several TFA approaches are based on the partitioning of the RVE into clusters, regions that exhibit similar strain responses under arbitrary loading conditions ,within which suitable approximations of the inelastic strain fields are introduced. The accuracy of TFA-based homogenization methods, as well as their computational efficiency, strongly depends on both the cluster definition and the adopted representation of the inelastic fields. In particular, approaches such as Piecewise Uniform Transformation Field Analysis (PWUTFA) assume a uniform inelastic field within each cluster. In this case, achieving accurate predictions typically requires a large number of clusters with an optimized spatial arrangement [2]. Alternatively, Mixed Transformation Field Analysis (MxTFA) allows for non-uniform stress and inelastic strain fields within each cluster, yielding higher accuracy than PWUTFA for the same number of clusters, albeit at the cost of increased computational effort. The present work aims to enhance the performance of PWUTFA while maintaining a limited number of clusters by developing a data-driven optimization procedure to propoerly modify the evaluation of the inelastic strain evolution within each cluster. The proposed approach consists of a two-step optimization process designed to minimize a global stress error metric between PWUTFA predictions and finite element reference solutions obtained from a set of pre-analyses. Several benchmark strain histories are employed in the online stage to validate the proposed data-driven strategy, and the results are compared with standard PWUTFA, MxTFA, and full finite element analyses.
