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- KurzbeschreibungThis book illustrates the deep roots of the geometrically nonlinear kinematics of<br>generalized continuum mechanics in differential geometry. Besides applications to first-<br>order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating<br>for generalized models of continuum mechanics such as second-order (gradient-type)<br>elasticity and elasto-plasticity.<br><br>After a motivation that arises from considering geometrically linear first- and second-<br>order crystal plasticity in Part I several concepts from differential geometry, relevant<br>for what follows, such as connection, parallel transport, torsion, curvature, and metric<br>for holonomic and anholonomic coordinate transformations are reiterated in Part II.<br>Then, in Part III, the kinematics of geometrically nonlinear continuum mechanics<br>are considered. There various concepts of differential geometry, in particular aspects<br>related to compatibility, are generically applied to the kinematics of first- and second-<br>order geometrically nonlinear continuum mechanics. Together with the discussion on<br>the integrability conditions for the distortions and double-distortions, the concepts<br>of dislocation, disclination and point-defect density tensors are introduced. For<br>concreteness, after touching on nonlinear first- and second-order elasticity, a detailed<br>discussion of the kinematics of (multiplicative) first- and second-order elasto-plasticity<br>is given. The discussion naturally culminates in a comprehensive set of different types<br>of dislocation, disclination and point-defect density tensors. It is argued, that these<br>can potentially be used to model densities of geometrically necessary defects and the<br>accompanying hardening in crystalline materials. Eventually Part IV summarizes the<br>above findings on integrability whereby distinction is made between the straightforward<br>conditions for the distortion and the double-distortion being integrable and the more<br>involved conditions for the strain (metric) and the double-strain (connection) being<br>integrable.<br><br>The book addresses readers with an interest in continuum modelling of solids from<br>engineering and the sciences alike, whereby a sound knowledge of tensor calculus and<br>continuum mechanics is required as a prerequisite.<br><br>
- AutorPaul Steinmann
- SerieLecture Notes in Applied Mathematics and Mechanics
- Seiten517 Seiten
- Gewicht825 g
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