Implicit Constitutive Modelling: Training Gated-Recurrent Units with Unlabeled Data and the Virtual Fields Method
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Constitutive models encode the stress-strain relationship of materials, which in plasticity depends on the loading history. Recurrent Neural Networks (RNNs) excel in capturing the effects of path-dependent behaviour, learning these relationships directly from data. Implicit constitutive modelling approaches based on ANNs typically rely on labelled data, from numerically generated datasets. However, certain variables like stresses are not measurable experimentally, requiring indirect training using measurable variables only. In this work, an RNN-based material model is trained from scratch using a novel indirect training approach, coupling the Virtual Fields Method (VFM). The RNN predicts the material tangent stiffness while the stress tensor is obtained from intermediate steps. Physics-based constraints are also softly imposed via penalty terms.
