The Virtual Fields Method to Indirectly Train Artificial Neural Networks for Implicit Constitutive Modelling

Artificial Neural Networks (ANNs) have the potential to provide a different approach constitutive modelling, with main advantage that these do not require postulate mathematical formulation or identify empirical parameters. Currently, training of an ANN for implicit modelling mostly relies on paired data, usually stress-strain however, stress cannot be directly measured in real experiment. As such, should carried out indirectly using measurable variables from experimental setting, such as displacements and applied force. In current work, global force data are used train predict state material. An test is recreated numerically order obtain displacement load distributions, i.e. obtaining synthetic virtual The strain previous time increments obtained corresponding inputs stress. Training without labels compute loss. Instead, local equilibrium conditions, application Virtual Fields Method (VFM) physical model, employed loss update network parameters, until predicted accurate.