Including Shear in a Neural Network Constitutive Model for Architectural Textiles

Even if a reliable constitutive modelling of materials is essential to finite element analyses, architectural textiles are still poorly described by making use of plane stress linear elastic models. More complex analytical models are computationally too expensive and require a large number of parameters to be calibrated, so that specific tests are often required, employing expensive and ad hoc designed equipment. The main reason for this is that coated textiles display a complex nonlinear, hysteretic, viscoelastic behaviour, which is difficult to model with classical analytical constitutive laws. In addition, coated fabrics involve aleatoric uncertainties due to the manufacturing process, as well as epistemic uncertainties related to the intrinsic difficulty of measuring certain quantities (e.g. the properties of yarns when embedded in a continuum matrix). Within this framework, Artificial Neural Networks (ANN) seem to be promising in reproducing the material mechanical behaviour, since they can be trained to learn the relation between input (strain) and output (stress) without the need of setting any explicit analytic stress-strain law. An existing ANN able to reproduce the biaxial tensile response of coated fabric membranes is here extended to include shear behaviour. After a description of the neural network architecture and its implementation, picture frame test data are employed for training and validation. The influence of different subdivisions of the experimental data into a training set, a validation set, and a testing set is investigated. Neural networks having different numbers of neurons are analysed, in order to establish the number of nodes required to accurately represent the experimental behaviour of the material, whilst avoiding overfitting at the same time.