LEADER 05584nam 22008535 450 001 9910438059303321 005 20251107172457.0 010 $a9786613844262 010 $a9781283531818 010 $a128353181X 010 $a9783642283536 010 $a3642283535 024 7 $a10.1007/978-3-642-28353-6 035 $a(CKB)2670000000232603 035 $a(EBL)972956 035 $a(OCoLC)804664632 035 $a(SSID)ssj0000740975 035 $a(PQKBManifestationID)11466879 035 $a(PQKBTitleCode)TC0000740975 035 $a(PQKBWorkID)10701640 035 $a(PQKB)11249683 035 $a(DE-He213)978-3-642-28353-6 035 $a(MiAaPQ)EBC972956 035 $a(PPN)168311801 035 $a(EXLCZ)992670000000232603 100 $a20120723d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFoundations of Micropolar Mechanics /$fby Victor A. Eremeyev, Leonid P. Lebedev, Holm Altenbach 205 $a1st ed. 2013. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013. 215 $a1 online resource (144 p.) 225 1 $aSpringerBriefs in Continuum Mechanics,$x2625-1337 300 $aDescription based upon print version of record. 311 08$a9783642283529 311 08$a3642283527 320 $aIncludes bibliographical references and index. 327 $aFoundations of Micropolar Mechanics; Preface; References; Contents; 1 Introduction; 2 Kinematics of Micropolar Continuum; References; 3 Forces and Couples, Stress and Couple Stress Tensors in Micropolar Continua; 3.1 Forces and Couples; 3.2 Euler's Laws of Motion; 3.3 Stress Tensor and Couple Stress Tensor; 3.4 Principal Stresses in Micropolar Continua; 3.5 Equations of Motion; 3.6 Boundary-Value Problems; References; 4 Constitutive Equations; 4.1 General Principles Restricting the Constitutive Equations; 4.2 Natural Lagrangian Strain Measures of Cosserat Continuum 327 $a4.2.1 Strain Measures by Geometrical Approach4.2.2 Principle of Virtual Work and Work-Conjugate Strain Measures; 4.2.3 Invariance of the Polar-Elastic Strain Energy Density; 4.2.4 Vectorial Parameterizations of Strain Measures; 4.3 Kinetic Constitutive Equations; 4.4 Material Symmetry Group; 4.5 Non-Linear Micropolar Isotropic Solids; 4.6 Physically Linear Micropolar Solid; 4.7 Linear Micropolar Isotropic Solids; 4.8 Constraints; 4.9 Constitutive Inequalities; 4.9.1 Constitutive Restrictions in Linear Micropolar Elasticity; 4.9.2 Coleman--Noll Inequality for Micropolar Continuum 327 $a4.9.3 Strong Ellipticity and Hadamard Inequality4.9.4 Ordinary Ellipticity; 4.10 Micropolar Fluid; 4.11 Some Sources of Constitutive Equations for Micropolar Materials; References; 5 Strong Ellipticity and AccelerationWaves in Micropolar Continuum; 5.1 Thermoconductivity Equation in the MicropolarContinuum; 5.2 Acceleration Waves; 5.3 Homothermal AccelerationWaves; Appendix A Elements of Tensor Analysis; A.1...Vectors; A.2...Tensorstensor; A.3...Second-Order Tensorssecond-order tensor; A.4...Higher Order Tensorstensor!higher order; A.5...Basis Transformation 327 $aA.6...Polar and Axial Vectors and Tensorsvector!axialtensor!axialvector!polartensor!polarA.7...Tensor Functions; A.8...Vector and Tensor Fields; A.9...Curves in Space; A.10...Surfaces; Appendix B Elements of Rigid Body Dynamics; Appendix C Elements of Mechanics of Elastic Rods; Appendix D Micropolar Plates and Shells as Two-Dimensional Cosserat Continua; D.1...Kinematics of a Micropolar Shell; D.2...The Virtual Work Principle and Formulation of Boundary Value Problems; D.3...Euler's Motion Laws of a Micropolar Shell; D.4...Constitutive Equations for a Micropolar Shell; D.5...Linear Theory of Micropolar Shells 327 $aD.6...Constitutive Restrictions for Micropolar ShellsD.6.1enspLinear Theory of Micropolar Shell; D.6.2enspColeman--Noll Inequality for Elastic ShellsColeman-Noll inequality; D.6.3enspStrong Ellipticity and Hadamard Inequality; D.6.4enspStrong Ellipticity Condition and Acceleration Wavesacceleration wave; D.6.5enspOrdinary Ellipticityordinary ellipticity; References; Index 330 $aThe book presents foundations of the micropolar continuum mechanics including a short but comprehensive introduction of stress and strain measures, derivation of motion equations and discussion of the difference between Cosserat and classical (Cauchy) continua, and the discussion of more specific problems related to the  constitutive modeling, i.e. constitutive inequalities, symmetry groups, acceleration waves, etc. 410 0$aSpringerBriefs in Continuum Mechanics,$x2625-1337 606 $aMechanics, Applied 606 $aSolids 606 $aMechanics 606 $aAlgebraic fields 606 $aPolynomials 606 $aSolid Mechanics 606 $aClassical Mechanics 606 $aField Theory and Polynomials 615 0$aMechanics, Applied. 615 0$aSolids. 615 0$aMechanics. 615 0$aAlgebraic fields. 615 0$aPolynomials. 615 14$aSolid Mechanics. 615 24$aClassical Mechanics. 615 24$aField Theory and Polynomials. 676 $a531 700 $aEremeyev$b Victor A$0931240 701 $aLebedev$b L. P$01089225 701 $aAltenbach$b Holm$f1956-$0762891 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438059303321 996 $aFoundations of micropolar mechanics$94187647 997 $aUNINA