{"product_id":"9783662464595","title":"Lecture Notes in Applied Mathematics and Mechanics: An Application to First- and Second-Order Elasticity and Elasto-Plasticity","description":"\u003ch1\u003eLecture Notes in Applied Mathematics and Mechanics: An Application to First- and Second-Order Elasticity and Elasto-Plasticity\u003c\/h1\u003e \u003ch2\u003eSteinmann, Paul\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eThis book illustrates the deep roots of the geometrically nonlinear kinematics of\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003egeneralized continuum mechanics in differential geometry. Besides applications to first-\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eorder elasticity and elasto-plasticity an appreciation thereof is particularly illuminating\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003efor generalized models of continuum mechanics such as second-order (gradient-type)\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eelasticity and elasto-plasticity.\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003e \u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eAfter a motivation that arises from considering geometrically linear first- and second-\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eorder crystal plasticity in Part I several concepts from differential geometry, relevant\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003efor what follows, such as connection, parallel transport, torsion, curvature, and metric\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003efor holonomic and anholonomic coordinate transformations are reiterated in Part II.\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eThen, in Part III, the kinematics of geometrically nonlinear continuum mechanics\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eare considered. There various concepts of differential geometry, in particular aspects\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003erelated to compatibility, are generically applied to the kinematics of first- and second-\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eorder geometrically nonlinear continuum mechanics. Together with the discussion on\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003ethe integrability conditions for the distortions and double-distortions, the concepts\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eof dislocation, disclination and point-defect density tensors are introduced. For\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003econcreteness, after touching on nonlinear fir\u003c\/b\u003e\u003c\/p\u003est- and second-order elasticity, a detailed\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003ediscussion of the kinematics of (multiplicative) first- and second-order elasto-plasticity\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eis given. The discussion naturally culminates in a comprehensive set of different types\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eof dislocation, disclination and point-defect density tensors. It is argued, that these\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003ecan potentially be used to model densities of geometrically necessary defects and the\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eaccompanying hardening in crystalline materials. Eventually Part IV summarizes the\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eabove findings on integrability whereby distinction is made between the straightforward\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003econditions for the distortion and the double-distortion being integrable and the more\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003einvolved conditions for the strain (metric) and the double-strain (connection) being\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eintegrable.\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003e \u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eThe book addresses readers with an interest in continuum modelling of solids from\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eengineering and the sciences alike, whereby a sound knowledge of tensor calculus and\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003econtinuum mechanics is required as a prerequisite.\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2015-04-07\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783662464595\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-662-46460-1\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 517\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":47729269735564,"sku":"9783662464595","price":179.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783662464595.jpg?v=1776882629","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783662464595","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}