Data-driven homogenisation of viscoelastic porous elastomers: Feedforward versus knowledge-based neural networks

• The response of the unit cell of a low-porosity viscous elastomer is computed. • The response to arbitrary, random histories of macroscopic strain is simulated. • Two different machine learning approaches are applied to the data generated. • We obtain two surrogate models of exceptional accuracy. • We show that knowledge-based machine learning can outperform feed-forward NNs. A computational framework is established to implement time-dependent data-driven surrogate constitutive models for the homogenised mechanical response of porous elastomers at large strains. The aim is to enhance the computational efficiency of multiscale analyses through the use of these surrogate models. To achieve this, explicit finite element (FE) simulations are conducted to predict the homogenised response of a cubic unit cell of a porous elastomer, using two different viscoelastic descriptions of the parent material, subject to pseudo-random, multiaxial, non-proportional histories of macroscopic strains. The histories of homogenised variables extracted from each set of FE predictions form a training dataset, which is used to train two different surrogate models, both relying on artificial neural networks (NNs). The first model predicts the increment in macroscopic stress over a simulation step, as a function of the macroscopic stress and strain at the beginning of the step, of the prescribed macroscopic strain increment, and of the corresponding time increment. The second model uses the same inputs and outputs but tests a knowledge-based modelling approach: it relies on the aid of an additional nonlinear elastic constitutive model, which is time- and path-independent and known a priori. This model represents an existing base of knowledge which is augmented and corrected by a NN after training on viscoelastic data. The data-driven surrogate model, therefore, learns the viscoelastic behaviour of the unit cell starting from knowledge of its elastic response. The two surrogate models are found to have comparable and very high accuracies, capturing the response of the homogenised unit cell to complex loading histories. Hyperparameter optimisation shows that the second, knowledge-based model requires a simpler NN and therefore incurs a smaller computational cost.