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This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations. Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals. This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.

Crystals -- Mechanical properties. --- Nonlinear mechanics. --- Engineering & Applied Sciences --- Chemical & Materials Engineering --- Materials Science --- Applied Mathematics --- Crystals --- Mechanical properties. --- Mechanics, Nonlinear --- Engineering. --- Crystallography. --- Continuum mechanics. --- Materials science. --- Continuum Mechanics and Mechanics of Materials. --- Characterization and Evaluation of Materials. --- Mechanics, Analytic --- Crystallography --- Powders --- Solids --- Mechanics. --- Mechanics, Applied. --- Surfaces (Physics). --- Solid Mechanics. --- Crystallography and Scattering Methods. --- Leptology --- Physical sciences --- Mineralogy --- Physics --- Surface chemistry --- Surfaces (Technology) --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Material science --- Solids. --- Materials—Analysis. --- Characterization and Analytical Technique. --- Solid state physics --- Transparent solids

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This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed ste

Geometry, Differential. --- Calculus of tensors. --- Continuum mechanics. --- Field theory (Physics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Differential geometry

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This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations. Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals. This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.

Fluid mechanics --- Chemical and physical cristallography --- Materials sciences --- kristallografie --- materiaalkennis --- mechanica

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Fragmentation reactions. --- Surfaces, Deformation of. --- Deformation potential. --- Fracture mechanics. --- Solids --- Concrete --- Thermal properties. --- Mechanical properties. --- Testing.

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Twinning (Crystallography) --- Computer simulation.