Mechanics and Thermodynamics of Mixtures with Continuous Diversity From Complex Media to Ice Sheets

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. Chapter 1 offers a critical discussion about the intricacies in the description of complex media as continuous bodies. Fundamentals on the homogenization (structural averaging) of porous materials are presented in a concise way. Chapter 2 gives an up-to-date review of the homogenization of polar granular media, with emphasis on the peculiarities of its microstructure. Chapter 3 combines the concepts of homogenization, polar media and chemical mixtures in a systematic manner, in order to derive appropriate balance equations for mixtures of microstructured media. Chapter 4 invokes the results of former chapters to resolve a contemporary polemic concerning energy invariance and inertial effects in chemically reacting mixtures of liquid crystals. Chapter 5 introduces the fundamental concepts of the thermodynamic theory of mixtures with continuous diversity from a generic perspective. Chapter 6 merges the formerly presented notions of microstructured media, chemically reacting mixtures and mixtures with continuous diversity into the powerful theory of hybrid mixtures with continuous diversity, or “doubly complex” media. Chapter 7 employs the theory of mixtures with continuous diversity to study the microstructure evolution of polymeric solutions, more precisely suspensions of rigid rodlike macromolecules. Chapter 8 demonstrates how the texture evolution of polycrystalline media undergoing recrystallization may be modeled by using the formalism of mixtures with continuous diversity. Besides a short historical synopsis of ice morphology research, the particular case of induced anisotropy and recrystallization in ice sheets is considered. Chapter 9 concludes this work with an overview on future applications, specially on the modeling of iceberg ensemble dynamics during Heinrich events, as well as on the study of abrasion, fragmentation and particle size segregation in polydisperse granular media. The most significative results of this dissertation comprehend: 1. the clarification of the similarities between homogenization (structural averaging) of microstructured media and the continuum description of chemical mixtures; 2. the solution of Müller’s paradox of frame dependence in chemically reacting mixtures of liquid crystals; 3. the thermodynamic theory of mixtures with continuous diversity;