{"product_id":"fundamentals-of-continuum-mechanics-isbn-9781118479919","title":"Fundamentals of Continuum Mechanics","description":"\u003cp\u003e\u003cb\u003eA concise introductory course text on continuum mechanics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eFundamentals of Continuum Mechanics\u003c\/i\u003e focuses on the fundamentals of the subject and provides the background for formulation of numerical methods for large deformations and a wide range of material behaviours. It aims to provide the foundations for further study, not just of these subjects, but also the formulations for much more complex material behaviour and their implementation computationally. \u003c\/p\u003e \u003cp\u003eThis book is divided into 5 parts, covering mathematical preliminaries, stress, motion and deformation, balance of mass, momentum and energy, and ideal constitutive relations and is a suitable textbook for introductory graduate courses for students in mechanical and civil engineering, as well as those studying material science, geology and geophysics and biomechanics.  \u003c\/p\u003e \u003cul\u003e \u003cli\u003eA concise introductory course text on continuum mechanics\u003c\/li\u003e \u003cli\u003eCovers the fundamentals of continuum mechanics\u003c\/li\u003e \u003cli\u003eUses modern tensor notation\u003c\/li\u003e \u003cli\u003eContains problems and accompanied by a companion website hosting solutions\u003c\/li\u003e \u003cli\u003eSuitable as a textbook for introductory graduate courses for students in mechanical and civil engineering\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eNomenclature xv\u003c\/p\u003e \u003cp\u003eIntroduction 1\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart One Mathematical Preliminaries 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Vectors 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Examples 9\u003c\/p\u003e \u003cp\u003e1.1.1 9\u003c\/p\u003e \u003cp\u003e1.1.2 9\u003c\/p\u003e \u003cp\u003eExercises 9\u003c\/p\u003e \u003cp\u003eReference 11\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Tensors 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Inverse 15\u003c\/p\u003e \u003cp\u003e2.2 Orthogonal Tensor 16\u003c\/p\u003e \u003cp\u003e2.3 Principal Values 16\u003c\/p\u003e \u003cp\u003e2.4 Nth-Order Tensors 18\u003c\/p\u003e \u003cp\u003e2.5 Examples 18\u003c\/p\u003e \u003cp\u003e2.5.1 18\u003c\/p\u003e \u003cp\u003e2.5.2 18\u003c\/p\u003e \u003cp\u003eExercises 19\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Cartesian Coordinates 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Base Vectors 21\u003c\/p\u003e \u003cp\u003e3.2 Summation Convention 23\u003c\/p\u003e \u003cp\u003e3.3 Tensor Components 24\u003c\/p\u003e \u003cp\u003e3.4 Dyads 25\u003c\/p\u003e \u003cp\u003e3.5 Tensor and Scalar Products 27\u003c\/p\u003e \u003cp\u003e3.6 Examples 29\u003c\/p\u003e \u003cp\u003e3.6.1 29\u003c\/p\u003e \u003cp\u003e3.6.2 29\u003c\/p\u003e \u003cp\u003e3.6.3 29\u003c\/p\u003e \u003cp\u003eExercises 30\u003c\/p\u003e \u003cp\u003eReference 30\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Vector (Cross) Product 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Properties of the Cross Product 32\u003c\/p\u003e \u003cp\u003e4.2 Triple Scalar Product 33\u003c\/p\u003e \u003cp\u003e4.3 Triple Vector Product 33\u003c\/p\u003e \u003cp\u003e4.4 Applications of the Cross Product 34\u003c\/p\u003e \u003cp\u003e4.4.1 Velocity due to Rigid Body Rotation 34\u003c\/p\u003e \u003cp\u003e4.4.2 Moment of a Force P about O 35\u003c\/p\u003e \u003cp\u003e4.5 Non-orthonormal Basis 36\u003c\/p\u003e \u003cp\u003e4.6 Example 37\u003c\/p\u003e \u003cp\u003eExercises 37\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Determinants 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Cofactor 42\u003c\/p\u003e \u003cp\u003e5.2 Inverse 43\u003c\/p\u003e \u003cp\u003e5.3 Example 44\u003c\/p\u003e \u003cp\u003eExercises 44\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Change of Orthonormal Basis 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Change of Vector Components 48\u003c\/p\u003e \u003cp\u003e6.2 Definition of a Vector 50\u003c\/p\u003e \u003cp\u003e6.3 Change of Tensor Components 50\u003c\/p\u003e \u003cp\u003e6.4 Isotropic Tensors 51\u003c\/p\u003e \u003cp\u003e6.5 Example 52\u003c\/p\u003e \u003cp\u003eExercises 53\u003c\/p\u003e \u003cp\u003eReference 56\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Principal Values and Principal Directions 57\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Example 59\u003c\/p\u003e \u003cp\u003eExercises 60\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Gradient 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Example: Cylindrical Coordinates 66\u003c\/p\u003e \u003cp\u003eExercises 67\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart Two Stress 69\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Traction and Stress Tensor 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Types of Forces 71\u003c\/p\u003e \u003cp\u003e9.2 Traction on Different Surfaces 73\u003c\/p\u003e \u003cp\u003e9.3 Traction on an Arbitrary Plane (Cauchy Tetrahedron) 75\u003c\/p\u003e \u003cp\u003e9.4 Symmetry of the Stress Tensor 76\u003c\/p\u003e \u003cp\u003eExercise 77\u003c\/p\u003e \u003cp\u003eReference 77\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Principal Values of Stress 79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Deviatoric Stress 80\u003c\/p\u003e \u003cp\u003e10.2 Example 81\u003c\/p\u003e \u003cp\u003eExercises 82\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Stationary Values of Shear Traction 83\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Example: Mohr–Coulomb Failure Condition 86\u003c\/p\u003e \u003cp\u003eExercises 88\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Mohr’s Circle 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eExercises 93\u003c\/p\u003e \u003cp\u003eReference 93\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart Three Motion and Deformation 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Current and Reference Configurations 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Example 102\u003c\/p\u003e \u003cp\u003eExercises 103\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Rate of Deformation 105\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Velocity Gradients 105\u003c\/p\u003e \u003cp\u003e14.2 Meaning of D 106\u003c\/p\u003e \u003cp\u003e14.3 Meaning of W 108\u003c\/p\u003e \u003cp\u003eExercises 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Geometric Measures of Deformation 111\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Deformation Gradient 111\u003c\/p\u003e \u003cp\u003e15.2 Change in Length of Lines 112\u003c\/p\u003e \u003cp\u003e15.3 Change in Angles 113\u003c\/p\u003e \u003cp\u003e15.4 Change in Area 114\u003c\/p\u003e \u003cp\u003e15.5 Change in Volume 115\u003c\/p\u003e \u003cp\u003e15.6 Polar Decomposition 116\u003c\/p\u003e \u003cp\u003e15.7 Example 118\u003c\/p\u003e \u003cp\u003eExercises 118\u003c\/p\u003e \u003cp\u003eReferences 120\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Strain Tensors 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Material Strain Tensors 121\u003c\/p\u003e \u003cp\u003e16.2 Spatial Strain Measures 123\u003c\/p\u003e \u003cp\u003e16.3 Relations Between D and Rates of E\u003csup\u003eG \u003c\/sup\u003eand U 124\u003c\/p\u003e \u003cp\u003e16.3.1 Relation Between Ė and D 124\u003c\/p\u003e \u003cp\u003e16.3.2 Relation Between D and U 125\u003c\/p\u003e \u003cp\u003eExercises 126\u003c\/p\u003e \u003cp\u003eReferences 128\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Linearized Displacement Gradients 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Linearized Geometric Measures 130\u003c\/p\u003e \u003cp\u003e17.1.1 Stretch in Direction N 130\u003c\/p\u003e \u003cp\u003e17.1.2 Angle Change 131\u003c\/p\u003e \u003cp\u003e17.1.3 Volume Change 131\u003c\/p\u003e \u003cp\u003e17.2 Linearized Polar Decomposition 132\u003c\/p\u003e \u003cp\u003e17.3 Small-Strain Compatibility 133\u003c\/p\u003e \u003cp\u003eExercises 135\u003c\/p\u003e \u003cp\u003eReference 135\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart Four Balance of Mass, Momentum, and Energy 137\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Transformation of Integrals 139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eExercises 142\u003c\/p\u003e \u003cp\u003eReferences 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Conservation of Mass 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Reynolds’ Transport Theorem 148\u003c\/p\u003e \u003cp\u003e19.2 Derivative of an Integral over a Time-Dependent Region 149\u003c\/p\u003e \u003cp\u003e19.3 Example: Mass Conservation for a Mixture 150\u003c\/p\u003e \u003cp\u003eExercises 151\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Conservation of Momentum 153\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Momentum Balance in the Current State 153\u003c\/p\u003e \u003cp\u003e20.1.1 Linear Momentum 153\u003c\/p\u003e \u003cp\u003e20.1.2 Angular Momentum 154\u003c\/p\u003e \u003cp\u003e20.2 Momentum Balance in the Reference State 155\u003c\/p\u003e \u003cp\u003e20.2.1 Linear Momentum 156\u003c\/p\u003e \u003cp\u003e20.2.2 Angular Momentum 157\u003c\/p\u003e \u003cp\u003e20.3 Momentum Balance for a Mixture 158\u003c\/p\u003e \u003cp\u003eExercises 159\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Conservation of Energy 161\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Work-Conjugate Stresses 163\u003c\/p\u003e \u003cp\u003eExercises 165\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart Five Ideal Constitutive Relations 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Fluids 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Ideal Frictionless Fluid 169\u003c\/p\u003e \u003cp\u003e22.2 Linearly Viscous Fluid 171\u003c\/p\u003e \u003cp\u003e22.2.1 Non-steady Flow 173\u003c\/p\u003e \u003cp\u003eExercises 175\u003c\/p\u003e \u003cp\u003eReference 176\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Elasticity 177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 Nonlinear Elasticity 177\u003c\/p\u003e \u003cp\u003e23.1.1 Cauchy Elasticity 177\u003c\/p\u003e \u003cp\u003e23.1.2 Green Elasticity 178\u003c\/p\u003e \u003cp\u003e23.1.3 Elasticity of Pre-stressed Bodies 179\u003c\/p\u003e \u003cp\u003e23.2 Linearized Elasticity 182\u003c\/p\u003e \u003cp\u003e23.2.1 Material Symmetry 183\u003c\/p\u003e \u003cp\u003e23.2.2 Linear Isotropic Elastic Constitutive Relation 185\u003c\/p\u003e \u003cp\u003e23.2.3 Restrictions on Elastic Constants 186\u003c\/p\u003e \u003cp\u003e23.3 More Linearized Elasticity 187\u003c\/p\u003e \u003cp\u003e23.3.1 Uniqueness of the Static Problem 188\u003c\/p\u003e \u003cp\u003e23.3.2 Pressurized Hollow Sphere 189\u003c\/p\u003e \u003cp\u003eExercises 191\u003c\/p\u003e \u003cp\u003eReference 194\u003c\/p\u003e \u003cp\u003eIndex 195\u003c\/p\u003e \u003cp\u003e“Motivated students will benefit from this systematic, disciplined and concise treatment of the fundamentals of continuum mechanics. Many practitioners will also appreciate the logical organization, and the lucid descriptions of such matters as the distinctions between the various common stress and strain measures.”  (\u003ci\u003ePure and Applied Geophysics\u003c\/i\u003e, 1 November 2015)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e  \u003cb\u003eJohn W. Rudnicki\u003c\/b\u003e received his bachelor, master’s and PhD degrees from Brown University in the USA, the last in 1977. He has been on the faculty of Northwestern University since 1981, where he is now Professor of Civil and Environmental Engineering and Mechanical Engineering. He is a Fellow of the American Society of Mechanical Engineers. He has been awarded the Biot Medal from the American Society of Civil Engineers, the Brown Engineering Alumni Medal, the Daniel C. Drucker Medal from the American Society of Mechanical Engineers, and the Engineering Science Medal from the Society of Engineering Science. His research has been primarily in geomechanics, specifically the inelastic behavior and failure of geomaterials. He has been especially interested in deformation instabilities in brittle rocks and granular media, including their interactions with pore fluids, with applications to the mechanics of earthquakes and environment- and resource-related geomechanics  \u003cp\u003eContinuum mechanics is a mathematical framework for studying the transmission of force through and deformation of materials of all types. The goal is to construct a framework that is free of special assumptions about the type of material, the size of deformations, the geometry of the problem, etc. Of course, no real materials are actually continuous; nevertheless, treating the material as continuous is a great advantage since it makes possible the use of mathematical tools of continuous functions, such as differentiation. In addition to being convenient, this approach works remarkably well. This is true even at size scales for which the justification of treating the material as a continuum might be debatable. The ultimate justification is that predictions made using continuum mechanics are in accord with observations and measurements. \u003c\/p\u003e \u003cp\u003e\u003ci\u003eFundamentals of Continuum Mechanics\u003c\/i\u003e comprehensively introduces the subject and the background for formulation of numerical methods for large deformations and a wide range of material behaviors. It provides the foundations for further study, not just of these subjects, but also for formulations of more complex material behavior and their implementation computationally. It is divided into five parts, covering mathematical preliminaries; stress; motion and deformation; balance of mass, momentum, and energy; and ideal constitutive relations. \u003c\/p\u003e \u003cp\u003eKey features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eServes as a concise introductory course text on continuum mechanics.\u003c\/li\u003e \u003cli\u003eCovers the fundamentals of continuum mechanics.\u003c\/li\u003e \u003cli\u003eUses modern tensor notation.\u003c\/li\u003e \u003cli\u003eContains problems and is accompanied by a companion website hosting solutions.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eFundamentals of Continuum Mechanics\u003c\/i\u003e is an ideal textbook for introductory graduate courses for students in mechanical and civil engineering, as well as those studying materials science, geology and geophysics, and biomechanics. It is also a concise reference for industry practitioners.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989257699557,"sku":"NP9781118479919","price":80.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118479919.jpg?v=1761783408","url":"https:\/\/k12savings.com\/products\/fundamentals-of-continuum-mechanics-isbn-9781118479919","provider":"K12savings","version":"1.0","type":"link"}