On adaptive thermo-electro-elasticity within a Green-Naghdi type II or III theory

We develop a thermo-electro-mechanical continuum theory for a bone remodeling model in order to understand and predict the features of the remodeling process under the control of the strain for a normal living bone. Bone remodeling refers to the continual processes of growth, reinforcement and resorption which arise in living bone. Unlike other approaches to the subject, we follow the Green-Naghdi approach to thermodynamics that employs the concept of thermal displacement and an entropy equality instead of an entropy inequality. We study the bone remodeling process in the context of thermo-electro-elasticity and introduce new balance laws of momentum, energy and entropy. Then, we derive the local balance laws, the constitutive assumptions, the constitutive restrictions and finally focus on the case of transversely isotropic bodies. Last but not least, we prove that the mathematical model is well posed in the nonlinear case.