ABSTRACT
ABSTRACT: The aim of the paper is the presentation of a thermodynamically consistent weakly-nonlocal (gradient type) modeling of materials characterized by translational and rotational degrees of freedom of material particles in the physical space and dissipative changes of the internal structure caused by material micro-forces and micro-couples. These properties can be observed for a wide range of media including concrete, rocks, sands and polycrystalline metals. Since these materials under external actions localize in bands of intensive shearing or narrow zones of micro-cracking often the precursor of macro-failure, we formulate a gradient model to capture appropriately localization phenomena. To describe the translational and rotational motion of material particles on the macro-level, a theory of oriented media is formulated including a length scale associated with the size of material particles. Taking into account that inhomogeneities on the mesolevel as micro-shearbands, -cracks, -voids, dislocations and disclinations and their time changes are caused by dissipative driving forces and couples in the material space, we postulate two additional balance laws of material forces and couples introducing in this way two additional length scales. Next, the first and second law of thermodynamics for physical and material space are formulated with the entropy production as a measure of non-equilibrium. Furthermore, general constitutive equations consistent with the second law of thermodynamics are formulated and some special cases are considered.
