Foundations of micropolar mechanics / / Victor A. Eremeyev, Leonid P. Lebedev, Holm Altenbach

• Record Nr.: UNINA9910438059303321
• Autore: Eremeyev Victor A
• Pubbl/distr/stampa: Heidelberg, : Springer, 2012, c2013
• ISBN: 1-283-53181-X; 9786613844262; 3-642-28353-5
• Edizione: [1st ed. 2013.]
• Descrizione fisica: 1 online resource (144 p.)
• Collana: SpringerBriefs in applied sciences and technology. Continuum mechanics, , 2191-530x
• Altri autori (Persone): LebedevL. P; AltenbachHolm <1956->
• Disciplina: 531
• Soggetti: Continuum mechanics; Micropolar elasticity
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Foundations 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; 4.2.1 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; 4.9.3 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; A.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; D.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
• Sommario/riassunto: The 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.