LEADER 05456nam 22007812 450 001 9910790281003321 005 20151005020622.0 010 $a1-107-08481-4 010 $a1-107-22440-3 010 $a1-280-39347-5 010 $a9786613571397 010 $a1-139-33727-0 010 $a1-139-33972-9 010 $a0-511-98012-4 010 $a1-139-34130-8 010 $a1-139-33640-1 010 $a1-139-33814-5 035 $a(CKB)2670000000177945 035 $a(EBL)866887 035 $a(OCoLC)792684474 035 $a(SSID)ssj0000655055 035 $a(PQKBManifestationID)11395516 035 $a(PQKBTitleCode)TC0000655055 035 $a(PQKBWorkID)10595485 035 $a(PQKB)10633481 035 $a(UkCbUP)CR9780511980121 035 $a(MiAaPQ)EBC866887 035 $a(MiAaPQ)EBC5120012 035 $a(Au-PeEL)EBL866887 035 $a(CaPaEBR)ebr10558220 035 $a(Au-PeEL)EBL5120012 035 $a(CaONFJC)MIL357139 035 $a(PPN)261372823 035 $a(EXLCZ)992670000000177945 100 $a20101014d2012|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aContinuum mechanics in the earth sciences /$fWilliam I. Newman$b[electronic resource] 205 $a1st ed. 210 1$aCambridge :$cCambridge University Press,$d2012. 215 $a1 online resource (xii, 182 pages) $cdigital, PDF file(s) 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-56289-9 320 $aIncludes bibliographical references and index. 327 $aCover; CONTINUUM MECHANICS IN THE EARTH SCIENCES; Title; Copyright; Dedication; Contents; Preface; Acknowledgements; 1 Some mathematical essentials; 1.1 Scalars, vectors, and Cartesian tensors; 1.2 Matrices and determinants; 1.3 Transformations of Cartesian tensors; 1.4 Eigenvalues and eigenvectors; 1.5 Simplified approach to rotation; 1.6 Curvature, torsion, and kinematics; Exercises; 2 Stress principles; 2.1 Body and surface forces; 2.2 Cauchy stress principle; 2.3 Stress tensor; 2.4 Symmetry and transformation laws; 2.5 Principal stresses and directions 327 $a2.6 Solving the cubic eigenvalue equation problem2.7 Maximum and minimum stress values; 2.8 Mohr's circles; Exercises; 3 Deformation and motion; 3.1 Coordinates and deformation; 3.2 Strain tensor; 3.3 Linearized deformation theory; 3.4 Stretch ratios; 3.5 Velocity gradient; 3.6 Vorticity and material derivative; Exercises; 4 Fundamental laws and equations; 4.1 Terminology and material derivatives; 4.2 Conservation of mass and the continuity equation; 4.3 Linear momentum and the equations of motion; 4.4 Piola-Kirchhoff stress tensor; 4.5 Angular momentum principle 327 $a4.6 Conservation of energy and the energy equation4.7 Constitutive equations; 4.8 Thermodynamic considerations; Exercises; 5 Linear elastic solids; 5.1 Elasticity, Hooke's law, and free energy; 5.2 Homogeneous deformations; 5.3 Role of temperature; 5.4 Elastic waves for isotropic bodies; 5.5 Helmholtz's decomposition theorem; 5.6 Statics for isotropic bodies; 5.7 Microscopic structure and dislocations; Exercises; 6 Classical fluids; 6.1 Stokesian and Newtonian fluids: Navier-Stokes equations; 6.2 Some special fluids and flows; Exercises; 7 Geophysical fluid dynamics 327 $a7.1 Dimensional analysis and dimensionless form7.2 Dimensionless numbers; Exercises; 8 Computation in continuum mechanics; 8.1 Review of partial differential equations; 8.2 Survey of numerical methods; 9 Nonlinearity in the Earth; 9.1 Friction; 9.2 Fracture; 9.3 Percolation and self-organized criticality; 9.4 Fractals; References; Index 330 $aContinuum mechanics underlies many geological and geophysical phenomena, from earthquakes and faults to the fluid dynamics of the Earth. This interdisciplinary book provides geoscientists, physicists and applied mathematicians with a class-tested, accessible overview of continuum mechanics. Starting from thermodynamic principles and geometrical insights, the book surveys solid, fluid and gas dynamics. In later review chapters, it explores new aspects of the field emerging from nonlinearity and dynamical complexity and provides a brief introduction to computational modeling. Simple, yet rigorous, derivations are used to review the essential mathematics. The author emphasizes the full three-dimensional geometries of real-world examples, enabling students to apply this in deconstructing solid earth and planet-related problems. Problem sets and worked examples are provided, making this a practical resource for graduate students in geophysics, planetary physics and geology and a beneficial tool for professional scientists seeking a better understanding of the mathematics and physics within Earth sciences. 606 $aContinuum mechanics 606 $aGeophysics$xMathematics 606 $aPlanetary theory$xMathematics 606 $aGeology$xMathematics 615 0$aContinuum mechanics. 615 0$aGeophysics$xMathematics. 615 0$aPlanetary theory$xMathematics. 615 0$aGeology$xMathematics. 676 $a531 700 $aNewman$b William I.$0214780 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910790281003321 996 $aContinuum mechanics in the earth sciences$93688894 997 $aUNINA