9783662464595 - Geometrical Foundations of Continuum Mechanics: An Application to First- and Second-Order Elasticity and Elasto-Plasticity (Lecture Notes in Applied Mathematics and... (9 Ergebnisse)

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Taschenbuch. Zustand: Neu. Geometrical Foundations of Continuum Mechanics | An Application to First- and Second-Order Elasticity and Elasto-Plasticity | Paul Steinmann | Taschenbuch | xxiv | Englisch | 2015 | Springer | EAN 9783662464595 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book illustrates the deep roots of the geometrically nonlinear kinematics ofgeneralized continuum mechanics in differential geometry. Besides applications to first-order elasticity and elasto-plasticity an appreciation thereof is particularly illuminatingfor generalized models of continuum mechanics such as second-order (gradient-type)elasticity and elasto-plasticity. After a motivation that arises from considering geometrically linear first- and second-order crystal plasticity in Part I several concepts from differential geometry, relevantfor what follows, such as connection, parallel transport, torsion, curvature, and metricfor holonomic and anholonomic coordinate transformations are reiterated in Part II.Then, in Part III, the kinematics of geometrically nonlinear continuum mechanicsare considered. There various concepts of differential geometry, in particular aspectsrelated to compatibility, are generically applied to the kinematics of first- and second-order geometrically nonlinear continuum mechanics. Together with the discussion onthe integrability conditions for the distortions and double-distortions, the conceptsof dislocation, disclination and point-defect density tensors are introduced. Forconcreteness, after touching on nonlinear first- and second-order elasticity, a detaileddiscussion of the kinematics of (multiplicative) first- and second-order elasto-plasticityis given. The discussion naturally culminates in a comprehensive set of different typesof dislocation, disclination and point-defect density tensors. It is argued, that thesecan potentially be used to model densities of geometrically necessary defects and theaccompanying hardening in crystalline materials. Eventually Part IV summarizes theabove findings on integrability whereby distinction is made between the straightforwardconditions for the distortion and the double-distortion being integrable and the moreinvolved conditions for the strain (metric) and the double-strain (connection) beingintegrable. The book addresses readers with an interest in continuum modelling of solids fromengineering and the sciences alike, whereby a sound knowledge of tensor calculus andcontinuum mechanics is required as a prerequisite.

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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book illustrates the deep roots of the geometrically nonlinear kinematics ofgeneralized continuum mechanics in differential geometry. Besides applications to first-order elasticity and elasto-plasticity an appreciation thereof is particularly illuminatingfor generalized models of continuum mechanics such as second-order (gradient-type)elasticity and elasto-plasticity. After a motivation that arises from considering geometrically linear first- and second-order crystal plasticity in Part I several concepts from differential geometry, relevantfor what follows, such as connection, parallel transport, torsion, curvature, and metricfor holonomic and anholonomic coordinate transformations are reiterated in Part II.Then, in Part III, the kinematics of geometrically nonlinear continuum mechanicsare considered. There various concepts of differential geometry, in particular aspectsrelated to compatibility, are generically applied to the kinematics of first- and second-order geometrically nonlinear continuum mechanics. Together with the discussion onthe integrability conditions for the distortions and double-distortions, the conceptsof dislocation, disclination and point-defect density tensors are introduced. Forconcreteness, after touching on nonlinear first- and second-order elasticity, a detaileddiscussion of the kinematics of (multiplicative) first- and second-order elasto-plasticityis given. The discussion naturally culminates in a comprehensive set of different typesof dislocation, disclination and point-defect density tensors. It is argued, that thesecan potentially be used to model densities of geometrically necessary defects and theaccompanying hardening in crystalline materials. Eventually Part IV summarizes theabove findings on integrability whereby distinction is made between the straightforwardconditions for the distortion and the double-distortion being integrable and the moreinvolved conditions for the strain (metric) and the double-strain (connection) beingintegrable. The book addresses readers with an interest in continuum modelling of solids fromengineering and the sciences alike, whereby a sound knowledge of tensor calculus andcontinuum mechanics is required as a prerequisite. 544 pp. Englisch.

Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book illustrates the deep roots of the geometrically nonlinear kinematics ofgeneralized continuum mechanics in differential geometry. Besides applications to firstorder elasticity and elasto-plasticity an appreciation thereof is particularly illuminatingfor generalized models of continuum mechanics such as second-order (gradient-type)elasticity and elasto-plasticity.After a motivation that arises from considering geometrically linear first- and secondorder crystal plasticity in Part I several concepts from differential geometry, relevantfor what follows, such as connection, parallel transport, torsion, curvature, and metricfor holonomic and anholonomic coordinate transformations are reiterated in Part II.Then, in Part III, the kinematics of geometrically nonlinear continuum mechanicsare considered. There various concepts of differential geometry, in particular aspectsrelated to compatibility, are generically applied to the kinematics of first- and secondorder geometrically nonlinear continuum mechanics. Together with the discussion onthe integrability conditions for the distortions and double-distortions, the conceptsof dislocation, disclination and point-defect density tensors are introduced. Forconcreteness, after touching on nonlinear first- and second-order elasticity, a detaileddiscussion of the kinematics of (multiplicative) first- and second-order elasto-plasticityis given. The discussion naturally culminates in a comprehensive set of different typesof dislocation, disclination and point-defect density tensors. It is argued, that thesecan potentially be used to model densities of geometrically necessary defects and theaccompanying hardening in crystalline materials. Eventually Part IV summarizes theabove findings on integrability whereby distinction is made between the straightforwardconditions for the distortion and the double-distortion being integrable and the moreinvolved conditions for the strain (metric) and the double-strain (connection) beingintegrable.The book addresses readers with an interest in continuum modelling of solids fromengineering and the sciences alike, whereby a sound knowledge of tensor calculus andcontinuum mechanics is required as a prerequisite.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 544 pp. Englisch.