LEADER 05115nam 2200673Ia 450 001 9910438059303321 005 20200520144314.0 010 $a1-283-53181-X 010 $a9786613844262 010 $a3-642-28353-5 024 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 $a20120825h20122013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFoundations of micropolar mechanics /$fVictor A. Eremeyev, Leonid P. Lebedev, Holm Altenbach 205 $a1st ed. 2013. 210 $aHeidelberg $cSpringer$d2012,c2013 215 $a1 online resource (144 p.) 225 0$aSpringerBriefs in applied sciences and technology.$pContinuum mechanics,$x2191-530x 300 $aDescription based upon print version of record. 311 $a3-642-28352-7 320 $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,$x2625-1329 606 $aContinuum mechanics 606 $aMicropolar elasticity 615 0$aContinuum mechanics. 615 0$aMicropolar elasticity. 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