A perspective on statistical physics in constitutive modeling*

Constitutive models are required to complete the governing equations describing a material. While continuum mechanics and thermodynamics provide some guidelines for deriving these models, they provide no guidance on actually deriving a model from the molecules that constitute the material. In contrast, statistical physics allows thermodynamic quantities to be derived from molecular structure. Consequently, constitutive models have been successfully developed using features of statistical physics, and these models have many desirable thermodynamic characteristics as a direct result. However, since the molecular physics of a given material are extremely complicated, drastic simplifications must be made in order to actually obtain constitutive models. The task is therefore to prescribe the mechanics of molecules constituting the material with (1) sufficient complexity to capture the desired physics, and (2) sufficient simplicity such that the resulting constitutive model is still analytically tractable. This presentation will highlight this overall perspective on statistical physics in constitutive modeling while providing some examples from the literature.