Thermodynamics and Nonlocality in Continuum Physics

This paper is devoted to the modelling of nonlocality in continuum physics through constitutive functions that depend on suitable gradients. For definiteness, the attention is addressed to elastic solids, heat conductors, and magnetic solids. Models are developed where both the requirements of the second law of thermodynamics and the balance equations are satisfied for the constitutive functions that involve gradients of strain, temperature, heat flux, and magnetization. Concerning elastic and magnetic solids, it is shown that, depending on the chosen variables, the standard symmetry property of the stress holds identically. The models so developed are free from any hyperstress tensor frequently considered in the literature.