Thermodynamic modeling of fully coupled finite-deformation thermo-electro-magneto-mechanical behavior for multifunctional applications

In this paper, we model fully coupled thermo-electro-magneto-mechanical (TEMM) behavior in the finite-deformation regime by (i) developing for the first time a comprehensive catalogue of free energies, state variables, and state equations, and (ii) combining this catalogue with the first principles of nonlinear continuum electrodynamics. We develop our catalogue in a thermodynamically consistent manner, and circumvent the ambiguities and challenges inherent in nonlinear continuum electrodynamics, by connecting with classical equilibrium thermodynamics. We use its formalism as a blueprint for characterizing a fundamental energetic process, that is, one where internal energy is the characterizing potential, the independent variables are extensive, and the dependent variables are intensive. A key feature of identifying this fundamental energetic process is the resulting ability to transparently and rigorously introduce new free energies – many appearing in the finite-deformation TEMM literature for the first time – that employ any set of intensive or extensive quantities as independent variables. We also develop novel mathematical transformations that accommodate alternative electromagnetic work conjugates as independent variables.Each thermodynamic potential in our comprehensive catalogue characterizes a particular thermo-electro-magneto-mechanical process. Each process, in turn, correlates with a particular experiment, the independent variables being controlled and the dependent variables being the measured responses. Our framework will thus enable the development of constitutive models for multifunctional materials under different experimental conditions. Additionally, the research presented herein can be used to convert targeted performance properties that are inherently nonlinear, three dimensional, and anisotropic into a “recipe” for multifunctional material design.