Learning Viscoelastic Responses with a Thermodynamic Recurrent Neural Network with Maxwell Encoding

Neural network methods are increasingly used to build constitutive laws in computational mechanics [1]. Neural Networks may for instance be used a surrogates for micro-mechanical models, whereby evaluating the response of high-fidelity numerical representative volume elements proves prohibitively expensive. Alternatively, Neural Networks may be used whenever traditional phenomenological approaches to constitutive modelling fails, i.e. whenever one fails to find a functional form for the constitutive law that enables to represent the behaviour of the material faithfully over the entirety of possible loading scenarios. One example is the viscoelastic behaviour of polymers, which remains difficult to describe accurately. The state of the art on these machine learning methods for the prediction of behavioural laws with a dependence on loading history do not show models with both a strong interpolatory, extrapolatory capacity and with a number of data consistent with today’s experimental capabilities [2]. To enforce a better bias, one used mechanical knowledge by introducing some mechanical regularisation terms [3], [4] or to considered structural approaches [5]. In this work, we describe a novel Neural Network strategy that combines a Maxwell model, which is extensively used as to describe linear viscoelastic responses, and a Thermodynamic Recurrent Neural Network. The coupling between the phenomenological and data-driven blocks of our model is done in two ways. Firstly, the Neural Network, and more precisely LSTM cells, corrects the response provided by the Maxwell model, which closely resembles the residual connections