Mechanics and Thermodynamics of Mixtures with Continuous Diversity

The aim of this thesis is to introduce to the reader the thermodynamic theory of mixtures with continuous diversity and to illustrate its potential through applications to diverse complex media. The most significative results of this dissertation comprehend: the clarification of the similarities between homogenization (structural averaging) of microstructured media and the continuum description of chemical mixtures; the solution of Müller's paradox of frame dependence in chemically reacting mixtures of liquid crystals; the thermodynamic theory of mixtures with continuous diversity; the derivation of balance equations and jump conditions for chemically reacting mixtures of microstructured media; the development of a constitutive theory for polymeric solutions of rodlike macromolecules within the frames of the theory of mixtures with continuous diversity; the construction of a thermodynamically consistent continuum theory for creep and recrystallization of ice sheets; the outline of a description of abrasion and fragmentation from the viewpoint of mixtures with continuous diversity