Automatic Discovery of Interpretable Free Thermal Strain Models
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The thermomechanical behaviour of concrete at high temperatures is critical, as it may threaten structural safety and lead to significant economic losses. Despite numerous research efforts aimed at capturing free thermal strain behaviour [1], developing a single unified model applicable to all concrete mixes remains impractical. Adopting an inappropriate model may result in inaccurate and unsafe predictions. In this context, automatic discovery methods can be employed to discover interpretable constitutive models by leveraging a catalogue of candidate constitutive components, balance equations and sparse optimisation. This family of approaches was originally developed for identifying physical laws in dynamical systems and later extended to solid mechanics [2]. This study aims to extend automated discovery to thermo-mechanical constitutive modelling. To this end, a computational framework is developed that leverages coupled temperature and displacement datasets with their corresponding reaction forces, all of which can be realistically obtained in experiments. Specifically, the temperature field can be measured using infrared thermography or distributed thermocouples and is used to reveal the dominant terms in a library based on the thermoelastic strain energy density function. The problem is formulated as an optimisation task, with the cost function defined through the balance of linear momentum. To promote sparsity, an L^p-regularisation term, with 0
