| Preface | p. xiii |
| Introduction | p. 1 |
| The basic idea of a Cosserat model | p. 1 |
| A brief outline of the book | p. 3 |
| Notation | p. 9 |
| Basic Tensor Operations in Curvilinear Coordinates | p. 11 |
| Covariant and contravariant base vectors | p. 11 |
| Base tensors and components of tensors | p. 13 |
| Basic tensor operations | p. 15 |
| Covariant differentiation and Christoffel symbols | p. 17 |
| Three-Dimensional Continua | p. 19 |
| Configurations and motion | p. 19 |
| Balance laws | p. 21 |
| Invariance under superposed rigid body motions | p. 27 |
| Mechanical power | p. 34 |
| An alternative derivation of the balance laws | p. 35 |
| An averaged form of the balance of linear momentum | p. 37 |
| Anisotropic nonlinear elastic materials | p. 38 |
| Constraints | p. 40 |
| Initial and boundary conditions | p. 43 |
| Material Symmetry | p. 44 |
| Isotropic nonlinear elastic materials | p. 47 |
| A small strain theory | p. 51 |
| Small deformations superimposed on a large deformation | p. 54 |
| Pure bending of an orthotropic rectangular parallelepiped | p. 57 |
| Torsion of an orthotropic rectangular parallelepiped | p. 60 |
| Forced shearing vibrations of an orthotropic rectangular parallelepiped | p. 63 |
| Free isochoric vibrations of an isotropic cube | p. 65 |
| An orthotropic rectangular parallelepiped loaded by its own weight | p. 66 |
| An isotropic circular cylinder loaded by its own weight | p. 67 |
| Plane strain free vibrations of an isotropic solid circular cylinder | p. 68 |
| Dissipation inequality and material damping | p. 69 |
| Cosserat Shells | p. 73 |
| Description of a shell structure | p. 73 |
| The Cosserat model of a shell | p. 77 |
| Derivation of the balance laws from the three-dimensional theory | p. 80 |
| Balance laws by the direct approach | p. 87 |
| Invariance under superposed rigid body motions | p. 92 |
| Mechanical power | p. 93 |
| An alternative derivation of the balance laws | p. 95 |
| Anisotropic nonlinear elastic shells | p. 97 |
| Constraints | p. 100 |
| Initial and boundary conditions | p. 106 |
| Further restrictions on constitutive equations for shells constructed from homogeneous anisotropic nonlinear elastic materials | p. 108 |
| A small strain theory | p. 113 |
| Small deformations superimposed on a large deformation | p. 117 |
| Pure bending of an orthotropic rectangular plate | p. 121 |
| Torsion of an orthotropic rectangular plate | p. 129 |
| Forced shearing vibrations of an orthotropic rectangular plate | p. 134 |
| Free isochoric vibrations of an isotropic cube | p. 136 |
| An orthotropic rectangular plate loaded by its own weight | p. 137 |
| Elastic shells | p. 140 |
| Plane strain expansion of an isotropic circular cylindrical shell | p. 143 |
| Plane strain free vibrations of an isotropic solid circular cylinder | p. 147 |
| Expansion of an isotropic spherical shell | p. 149 |
| Free vibrations of an isotropic solid sphere | p. 156 |
| An isotropic circular cylindrical shell loaded by its own weight | p. 158 |
| Isotropic nonlinear elastic shells | p. 161 |
| A simple derivation of the local equations for shells | p. 163 |
| A brief summary of the equations for shells | p. 165 |
| Generalized membranes and membrane-like shells | p. 170 |
| Simple membranes | p. 172 |
| Expansion of an incompressible isotropic spherical shell | p. 175 |
| Bending of an orthotropic plate into a circular cylindrical surface | p. 179 |
| Linear theory of an isotropic plate | p. 183 |
| Dissipation inequality and material damping | p. 187 |
| Cosserat Rods | p. 191 |
| Description of a rod structure | p. 191 |
| The Cosserat model of a rod | p. 194 |
| Derivation of the balance laws from the three-dimensional theory | p. 197 |
| Balance laws by the direct approach | p. 204 |
| Invariance under superposed rigid body motions | p. 207 |
| Mechanical power | p. 208 |
| An alternative derivation of the balance laws | p. 210 |
| Anisotropic nonlinear elastic rods | p. 212 |
| Constraints | p. 216 |
| Initial and boundary conditions | p. 222 |
| Further restrictions on constitutive equations for rods constructed from homogeneous anisotropic nonlinear elastic materials | p. 224 |
| A small strain theory | p. 229 |
| Small deformations superimposed on a large deformation | p. 232 |
| Pure bending of an orthotropic beam with rectangular cross-section | p. 235 |
| Torsion of an orthotropic beam with rectangular cross-section | p. 243 |
| Inhomogeneous shear of an orthotropic beam with rectangular cross-section | p. 245 |
| Forced shearing vibrations of an orthotropic beam with rectangular cross-section | p. 247 |
| Free isochoric vibrations of an isotropic cube | p. 250 |
| An orthotropic beam with rectangular cross-section loaded by its own weight | p. 251 |
| Elastic rods | p. 254 |
| Plane strain expansion of an isotropic circular cylindrical shell | p. 256 |
| Plane strain free vibrations of an isotropic solid circular cylinder | p. 260 |
| An isotropic circular cylindrical shell loaded by its own weight | p. 262 |
| Isotropic nonlinear elastic rods | p. 265 |
| A simple derivation of the local equations for rods with rectangular cross-sections | p. 266 |
| A brief summary of the equations for rods | p. 270 |
| Linearized equations for beams with rectangular cross-sections | p. 275 |
| Bernoulli-Euler rods | p. 277 |
| Timoshenko rods | p. 283 |
| Generalized strings | p. 287 |
| Simple strings | p. 288 |
| Transverse loading of an isotropic beam with a rectangular cross-section | p. 290 |
| Linearized buckling equations | p. 293 |
| An intrinsic formulation of Bernoulli-Euler rods with symmetric cross-sections | p. 303 |
| Dissipation inequality and material damping | p. 309 |
| Cosserat Points | p. 311 |
| Description of a point-like structure | p. 311 |
| The Cosserat point model | p. 313 |
| Derivation of the balance laws from the three-dimensional theory | p. 315 |
| Balance laws by the direct approach | p. 319 |
| Invariance under superposed rigid body motions | p. 321 |
| Mechanical power | p. 322 |
| An alternative derivation of the balance laws | p. 323 |
| Anisotropic nonlinear elastic Cosserat points | p. 325 |
| Constraints | p. 328 |
| Initial Conditions | p. 333 |
| Further restrictions on constitutive equations for Cosserat points constructed from homogeneous anisotropic nonlinear elastic materials | p. 334 |
| A small strain theory | p. 336 |
| Small deformations superimposed on a large deformation | p. 337 |
| Forced shearing vibrations of an orthotropic rectangular parallelepiped | p. 340 |
| Free isochoric vibrations of an isotropic cube | p. 345 |
| Isotropic nonlinear elastic Cosserat points | p. 346 |
| A brief summary of the equations for Cosserat points | p. 347 |
| Dissipation inequality and material damping | p. 351 |
| Numerical Solutions using Cosserat Theories | p. 355 |
| The Cosserat approach to numerical solution procedures for problems in continuum mechanics | p. 355 |
| Formulation of the numerical solution of spherically symmetric problems using the theory of a Cosserat shell | p. 357 |
| Formulation of the numerical solution of string problems using the theory of a Cosserat point | p. 378 |
| Formulation of the numerical solution of rod problems using the theory of a Cosserat point | p. 394 |
| Formulation of the numerical solution of three-dimensional problems using the theory of a Cosserat point | p. 410 |
| Formulation of the numerical solution of two-dimensional problems using the theory of a Cosserat point | p. 418 |
| Tensors, Tensor Products and Tensor Operations in Three Dimensions | p. 429 |
| Vectors and vector operations | p. 429 |
| Tensors as linear operators | p. 430 |
| Tensor products (special case) | p. 430 |
| Indicial notation | p. 435 |
| Tensor products (general case) | p. 437 |
| Tensor transformation relations | p. 440 |
| Additional definitions and results | p. 442 |
| Summary of Tensor Operations in Specific Coordinate Systems | p. 447 |
| Cylindrical polar coordinates | p. 447 |
| Spherical polar coordinates | p. 449 |
| Exercises | p. 451 |
| Acknowledgments | p. 467 |
| References | p. 467 |
| Index | p. 475 |
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