In this paper we analyze elastic and anelastic deformations of a continuous system
with non-Euclidean structure. The focus of this study is the intrinsic material metric,
gαβ, for the measurement of distances between material particles in the reference
configuration. The main results of the theory of deformation are reformulated taking
into account the non-Euclidean structure. The consequences of the second law of
thermodynamics have been investigated both for thermoelastic and viscoanelastic
In this paper the problem of magnetically undeformable polarizable media in the presence of an electromagnetic field is analyzed from a thermodynamic viewpoint. The thermodynamic transformations are explicited as functions in the state space in which one of the variables, characterizing the magnetic polarization, is given as an internal variable. The entropy form along the thermodynamic transformation is calculated for para- and diamagnetic media and the necessary conditions for its existence are given.