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The identification of constitutive laws is ubiquitous in engineering: in modeling of materials, where experimental data are fitted to mathematical models or learning surrogate models to beat the FE2 computational cost of multiscale numerical simulations. However, these models of constitutive laws, unless equipped with a energetic formulation, are not necessarily consistent with (a) the second law of thermodynamics; (b) stability of the material under extreme applied strain; and (c) the mathematical theory underpinning the existence of a solution of the non-linear momentum balance equation. In this work, we present a causal and energetic formulation, consistent with the aforementioned properties, of learning a history-dependent constitutive law. Moreover, we empirically discover, and, under controllability assumptions, theoretically show that the internal variables that are inferred from a learned constitutive model are identifiable up to a linear transform. This characterisation of the class of internal variables sheds light on an equivalence class of models that lead to the same stress-strain map. The framework is deployed to learn the Taylor-averaged response of a polycrystalline magnesium unit cell. We achieve a 2% relative error in the prediction of the Taylor-averaged response.
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