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This book presents an introduction to the non-linear mechanics of materials, focusing on a unified energetical approach. It begins by summarizing the framework of a thermodynamic description of continua, including a description of the kinematics of deformation, and a summary of the equations of motion. After a short description of the motion of the system and the mechanical interaction, the book introduces the Lagrangean and Hamiltonian functionals of the system, transitioning to the quasistatic characterization with emphasis on the role of potential energy and pseudo-potential of dissipation. The framework is then extended to fracture and damage mechanics with a similar energetical approach proposed for material damage and wear. The book looks at homogenization in non-linear mechanics for locally plastic or damaged material with an analysis of stability and bifurcation of the equilibrium path. Lastly, inverse problems in non-linear mechanics are introduced using optimal control theory. All the concepts introduced in the book are illustrated using analytical solutions on beams, rods, plates, or using spherical and cylindrical symmetries. Graduate students and researchers working on continuum mechanics and interested in a deeper understanding of materials damage, wear, and fatigue will find this book instructive and informative.

Nonlinear mechanics. --- Continuum mechanics. --- Thermodynamics. --- Materials --- Mechanics, Applied. --- Solids. --- Mathematical physics. --- Metals. --- Continuum Mechanics. --- Materials Fatigue. --- Solid Mechanics. --- Mathematical Methods in Physics. --- Metals and Alloys. --- Fatigue.

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This book presents an introduction to the non-linear mechanics of materials, focusing on a unified energetical approach. It begins by summarizing the framework of a thermodynamic description of continua, including a description of the kinematics of deformation, and a summary of the equations of motion. After a short description of the motion of the system and the mechanical interaction, the book introduces the Lagrangean and Hamiltonian functionals of the system, transitioning to the quasistatic characterization with emphasis on the role of potential energy and pseudo-potential of dissipation. The framework is then extended to fracture and damage mechanics with a similar energetical approach proposed for material damage and wear. The book looks at homogenization in non-linear mechanics for locally plastic or damaged material with an analysis of stability and bifurcation of the equilibrium path. Lastly, inverse problems in non-linear mechanics are introduced using optimal control theory. All the concepts introduced in the book are illustrated using analytical solutions on beams, rods, plates, or using spherical and cylindrical symmetries. Graduate students and researchers working on continuum mechanics and interested in a deeper understanding of materials damage, wear, and fatigue will find this book instructive and informative.

Mathematical physics --- Fluid mechanics --- Thermodynamics --- Solid state physics --- Applied physical engineering --- Metallurgy --- thermodynamica --- toegepaste mechanica --- wiskunde --- fysica --- mechanica --- metalen --- Continuum mechanics. --- Thermodynamics. --- Materials --- Mechanics, Applied. --- Solids. --- Mathematical physics. --- Metals. --- Continuum Mechanics. --- Materials Fatigue. --- Solid Mechanics. --- Mathematical Methods in Physics. --- Metals and Alloys. --- Fatigue.

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This volume presents recent developments in the theory of defects and the mechanics of material forces. Most of the contributions were presented at the International Symposium on Defect and Material Forces (ISDMM2007), held in Aussois, France, March 25-29, 2007. The mechanics of material forces, originated in the works of Eshelby, provide a rational framework for the description of driving forces on evolving inhomogeneities and structural changes in continua. The general eshelbian mechanics formulation comes up with a unifying treatment of different phenomena like fracture and damage evolution, phase transitions, plasticity and dislocation motion, etc. The articles concern both theoretical and computational aspects of the material mechanics of defects. Among the addressed topics are fracture and damage, electromagnetoelasticity, plasticity, distributed dislocations, thermodynamics, poroelasticity, generalized continua, structural optimization, conservation laws and symmetries, multiscale approaches, and numerical solution strategies. This is a hardbound spin-off reprinted from The International Journal of Fracture 147:1-4.

Classical mechanics. Field theory --- Fluid mechanics --- Engineering sciences. Technology --- analyse (wiskunde) --- toegepaste mechanica --- systeemtheorie --- ingenieurswetenschappen --- mechanica --- informatietheorie