Towards thermoelasticity of fractal media

An extension and generalization of thermomechanics with internal variables and thermoelasticity to fractal porous media is outlined. First, a field form of the second law of thermodynamics is derived. In conradistinction to the conventional Clausius-Duhem inequality, it involves generalized rates of deformation and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any length-scale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. With a focus on thermoelasticity, a new form of Duhamel's differential equation of heat conduction is derived.