Constitutive Modeling of Woven Composites based on Artificial Neural Networks informed by Multi-scale Analyses
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Although composite materials are rapidly expanding in various engineering and industrial fields, their wide scale use is often hampered by the difficulties to predict their mechanical behavior. This issue mainly arises from the heterogeneous nature of these materials. To deal with this, multi-scale approaches are appropriate to determine the stress-strain response of composite materials upon complex loading paths while integrating the description of the microstructure as well as the constitutive laws of its components. However, the use of a multi-scale model in the context of structural applications remains computationally expensive, e.g., FE2 analyses. The present work rather proposes an alternative approach based on Artificial Neural Networks (ANNs) that learns from multi-scale analyses, a constitutive relationship at the macroscopic scale. The ANNs are constructed from the principles of thermodynamics to describe both state and evolution laws of specific quantities of interest acting as internal state variables at the macroscopic scale. Those can be tracked from multiscale analyses and used as data for training the ANNs. An implicit time integration procedure of the ANN constitutive laws is also proposed. The latter enables the use of such model in finite element analyses of large-scale structures. The proposed method is applied to the case of woven composites. In this purpose, a full-field multi-scale model is built from the unit cell of the microstructure integrating damage and inelastic deformations in its components. This multi-scale model is then utilized to generate the database for training and testing the ANNs, upon numerous random loading paths.
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