LEADER 04500nam 22007215 450 001 996418277303316 005 20200723120342.0 010 $a3-030-42683-1 024 7 $a10.1007/978-3-030-42683-5 035 $a(CKB)4100000011243376 035 $a(DE-He213)978-3-030-42683-5 035 $a(MiAaPQ)EBC6199427 035 $a(PPN)248394770 035 $a(EXLCZ)994100000011243376 100 $a20200513d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric Continuum Mechanics$b[electronic resource] /$fedited by Reuven Segev, Marcelo Epstein 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2020. 215 $a1 online resource (VII, 416 p. 75 illus., 28 illus. in color.) 225 1 $aAdvances in Continuum Mechanics,$x2524-4639 ;$v42 311 $a3-030-42682-3 327 $aPart I: Kinematics, Forces, and Stress Theory -- Manifolds of Mappings for Continuum Mechanics -- Notes on Global Stress and Hyper-Stress Theories -- Applications of Algebraic Topology in Elasticity -- De Donder Construction for Higher Jets -- Part II: Defects, Uniformity, and Homogeneity -- Regular and Singular Dislocations -- Homogenization of Edge-Dislocations as a Weak Limit of de-Rham Currents -- A Kinematics of Defects in Solid Crystals -- Limits of Distributed Dislocations in Geometric and Constitutive Paradigms -- On the Homogeneity of Non-Uniform Material Bodies. 330 $aThis contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest. 410 0$aAdvances in Continuum Mechanics,$x2524-4639 ;$v42 606 $aDifferential geometry 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aMechanics 606 $aMechanics, Applied 606 $aContinuum physics 606 $aMathematical physics 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aTheoretical and Applied Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15001 606 $aClassical and Continuum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P2100X 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 615 0$aDifferential geometry. 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 0$aMechanics. 615 0$aMechanics, Applied. 615 0$aContinuum physics. 615 0$aMathematical physics. 615 14$aDifferential Geometry. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 24$aTheoretical and Applied Mechanics. 615 24$aClassical and Continuum Physics. 615 24$aMathematical Applications in the Physical Sciences. 676 $a516.36 702 $aSegev$b Reuven$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aEpstein$b Marcelo$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418277303316 996 $aGeometric Continuum Mechanics$92351473 997 $aUNISA