This book deals with analytical models of hydrogen-induced stresses in metallic materials. The analytical models, which are presented in this first volume, are determined for isotropic metallic materials. In general, hydrogen is accumulated in metallic materials in the form of various types of molecules (e.g. hydrogen molecules, molecules of methane, molecules of water vapour, etc.). With regard to the analytical modelling of the hydrogen-induced stresses, the isotropic metallic material with finite dimensions is replaced by a multi-hollow system with infinite dimensions, which consists of an infinite isotropic metallic matrix with periodically distributed spherical hollows. The various types of molecules are then accumulated in these spherical hollows. The analytical determination of the hydrogen-induced stress-strain state is based on the cell model, which considers cubic cells with central spherical hollows. The analytical modelling results from mutually different mathematical procedures, which are applied to fundamental equations of solid continuum mechanics (Hookes law, Cauchys law and equilibrium equations). The hydrogen-induced stress-strain state is thus determined by several different solutions, which fulfil boundary conditions. Due to these different solutions, the principle of minimal total potential energy of an elastic solid body is then required to be considered. In addition to the hydrogen-induced stresses and strains, the analytical model of the hydrogen-induced crack formation is also presented. The analytical model of this crack formation includes the determination of the limit state with respect to the crack initiation and the mathematical description of the crack shape propagated in the isotropic metallic material. Results of this book are applicable within basic research (solid continuum mechanics, theoretical physics, materials science, etc.), within engineering practices and within the undergraduate and postgraduate studies at universities and research institutes.

This book is the fourth volume in a series of books that present original results in the study of analytical models of thermal stresses in composite materials. Within the analytical modelling, two- and three-component composites are replaced by multi-particle-matrix and multi-particle-envelope-matrix systems, respectively, which consist of isotropic and/or anisotropic components represented by spherical particles (without or with an envelope of the particle surface) periodically distributed in an infinite matrix. In addition to the thermal stresses, analytical models of thermal-stress induced phenomena (crack formation, limit state, energy barrier, strengthening, lifetime prediction) are also discussed. Illustrative examples of applications of these analytical models are examined against real engineering materials (superconductive and structural ceramic composites). Results of this book are applicable within basic research (solid continuum mechanics, theoretical physics, materials science and engineering) as well as within engineering practices.

This book is the third volume in a series of books that present original results in the study of analytical models of thermal stresses in composite materials. For the analytical models, an elastic solid continuum is represented by multi-particle-matrix and multi-particle-envelope-matrix systems which consist of components represented by spherical particles periodically distributed in an infinite matrix. The trilogy 'Analytical Models of Rhermal Stresses in Composite Materials I, II, III' thus represent an integrated scientific work with an interdisciplinary character.

This book presents original analytical models of thermal and phase-transformation-induced stresses in isotropic components of two-component materials with void defects (i.e., dual-phase steel, materials of the precipitate-matrix type, etc.). These defects (i.e., pores, flaws) are a consequence of technological processes (e.g., powder metallurgy processes). These stresses, which are observed during a cooling process, originate below the relaxation temperature of a two-component material. The thermal stresses are a consequence of different thermal expansion coefficients of material components. The phase-transformation-induced stresses are a consequence of different dimensions of crystalline lattices, which originate during a phase transformation. The void defects exhibit a significant influence on mechanical properties of materials, as well as on the thermal and phase-transformation-induced stresses. This influence is included within the analytical models in this book. Accordingly, this book can be considered to present unique analytical results. The analytical models result from a suitable model material system, which corresponds to real two-component materials. These models are determined by different mathematical procedures, which are applied to fundamental equations of solid continuum mechanics. These different procedures result in different partial differential equations with non-zero right-hand sides. These differential equations result in different mathematical solutions for the thermal and phase-transformation-induced stresses. Finally, due to these different solutions, the principle of minimum total potential energy of an elastic solid body is required to be considered. Results of this book are applicable within basic research (solid continuum mechanics, theoretical physics, materials science), as well as within the practice of engineering.

This new book deals with analytical models of thermal stresses in isotropic and anisotropic composite materials. These models are represented by isotropic and anisotropic multi- and one-particle-(envelope)-matrix systems along with related thermal-stress induced phenomena, which are themselves represented by elastic energy fluctuations, thermal-stress strengthening, critical particle and envelope radii regarding a crack formation, including a mathematical description of the crack shape.

This book presents analytical models of thermal stresses in two- and three-component composites with anisotropic components. Within the analytical modelling, the two- and three-component composites are replaced by a multi-particle-matrix and multi-particle-envelope-matrix systems, respectively. These model systems consist of anisotropic spherical particles (either without or with an envelope on the particle surface), which are periodically distributed in an anisotropic infinite matrix. The thermal stresses that originate below the relaxation temperature during a cooling process are a consequence of the difference in dimensions of the components. This difference is a consequence of different thermal expansion coefficients and/or a consequence of the phase-transformation induced strain, which is determined for anisotropic crystal lattices. The analytical modelling results from mutually different mathematical procedures, which are applied to fundamental equations of solid continuum mechanics (Hookes law for an anisotropic elastic solid continuum, Cauchys law, and compatibility and equilibrium equations). The thermal stress-strain state in each anisotropic component of the model systems is determined by several different solutions, which fulfill boundary conditions. Due to these different solutions, a principle of minimal total potential energy of an elastic solid body is then required to be considered. Results of this book are applicable within basic research (solid continuum mechanics, theoretical physics, materials science, etc.) as well as within the practice of engineering.

This book is the first volume of the trilogy Analytical models of thermal stresses in composite materials I, II, III , presenting, in each of the volumes, genuine results only created by the author. The fact that the author proceeds from fundamental equations of Mechanics of Solid Continuum confirms the genuineness of the results and accordingly establishment of new scientific school with an interdisciplinary character belonging to the scientific branch Applied Mechanics. As an imagination considered for the analytical models, an elastic solid continuum is represented by a multi-particle-(envelope)-matrix system consisting of components represented by spherical particles periodically distributed in an infinite matrix, without or with a spherical envelope on the surface of each of the spherical particles. The multi-particle-(envelope)-matrix system with different distribution of the spherical particles is considered as a model system for a determination of the thermal stresses in real composite materials with finite dimensions included in the categories.