# An Introduction to Modern Anistropic Elasticity

## Description

The author, a leading Russian authority in the field of elasticity, has obtained some fundamental results in the investigation of a number of general problems in the mechanics of solids, the theory of shells, biomechanics, and the mechanics of elastomers. Fundamental theoretical investigations were combined with the practical applications to real construction problems. This book deals with symmetry, linear anisotropic elasticity, constitutive equations, plane problems, anisotropic and reinforced shells, brittle fracture, Volterra's dislocations, etc.

248 pages,
© 1998

## Table of Contents:

Chapter I. Symmetry Considerations

1. Symmetry of finite bodies

2. Notion of a symmetry group

5. Symmetry of the physical properties of crystals. The Neumann principle

6. Curvilinear anisotropy

Chapter II. Linear Elasticity

1. Structure of Hooke’s law

2. Principal axes of anisotropy

3. Bounds on the variation of the components of a positive definite symmetric matrix

4. Bounds on the variation of the elastic constants. Volumetric and shearing strains

6. Transversally isotropic material

8. Reduction of the elastic moduli

9. Orthotropic cylinder under pressure

Chapter III. Nonlinear Elasticity

1. Main equations of the nonlinear theory of elasticity

3. Nonlinear orthotropic material

4. Transversally isotropic material

6. Construction of the strain-energy density function

7. Hollow cylinder of incompressible material

Chapter IV. Deformation Anisotropy

1. Perturbation of the equilibrium configuration of the body

2. Deformation anisotropy of an initially isotropic material

3. Elastomers reinforced with filaments

Chapter V. Thin Anisotropic Shells under Large Deformations

1. Deformation of a shell

2. Stress resultants and moments. Boundary force values

5. Nonlinear orthotropic shells

6. Nonlinear transversally isotropic shells

7. Isotropic incompressible material

8. Construction of strain-energy density functions

9. Uniform membrane state of a plate of incompressible transversally isotropic material

10. Axially symmetric deformation of a shell of revolution

Chapter VI. Reinforced Shells

1. Reinforcement in the middle surface

2. Extension of a cylindrical plate

3. Reinforcement of a cylindrical shell in the middle surface

4. Hollow conic shock-absorber reinforced in the middle surface

5. Reinforcing a shell uniformly through the thickness by inextensible cords

6. Bending of a cylindrical plate reinforced uniformly through the thickness

Chapter VII. Problems in Plane Elasticity (A Linear Approach)

1. Generalized plane strain and plane stress

4. Use of functions of a complex variable

5. Plane containing an elliptic hole. Rectilinear cut

Chapter VIII. Problems in Plane Elasticity (A Nonlinear Approach)

3. Physically linear problem

4. Plane with an elliptic hole

5. Plane with a rectilinear cut

Chapter IX. Nonlinear Theory of Cracks (Brittle Fracture)

1. A geometrically and physically nonlinear theory of cracks in an isotropic elastic material

2. On the nonlinear theory of cracks in an anisotropic material

Chapter X. Nonlinear Volterra’s Dislocations

1. Volterra’s dislocations in the linear theory of elasticity

2. Nonlinear dislocations and disclinations

4. Continuation (a weakly compressible material)

Chapter XI. Some Aspects of Theory

2. Semisymmetric tensor of rank four

7. Tensor functions of vector type

9. Work conjugates. Objective rates of change of stress

10. Stability of an anisotropic material

11. Stability of an isotropic material

12. Structural invariants of large deformations

13. “True” measures of stresses and strains