Anisotropic elasticity. Theory and applications.

*(English)*Zbl 0883.73001
Oxford Engineering Science Series. 45. Oxford: Oxford Univ. Press. xvii, 570 p. (1996).

The book is devoted to solutions of mainly two-dimensional problems in linear anisotropic elasticity, where there is a rich source of solutions and solving techniques such as the Lekhnitskij and Stroh formalism. Such items are not only important in the context of pure elasticity, but are also important tools for inclusion problems, fracture and damage mechanics, plasticity, and others. As the author argues, anisotropic solutions are in general simpler than the isotropic ones. He considers isotropy as a degenerate case of anisotropy, which reduces rather than produces clearity and simplicity of the behaviour of the corresponding field problem. In the book, an hommage to A. N. Stroh (1926-1962) is included which gives interesting information on the life and work of this important researcher.

In contrast to the rather general title, the book is restricted to the above items. The part on the material theory, e.g., is quite short. In addition, some of the widespread errors in this field are also reproduced in this book. For example, the symmetry of the elasticity tensor with respect to the first two indices is definitely not a consequence of the symmetry of the stress tensor. The fourth rank identity maps all symmetric tensors into symmetric ones, without having the left subsymmetry. Moreover, any tensor with this subsymmetry is singular, and hence, a compliance tensor as an inverse of the stiffness tensor would not exist in this case.

As the book considers mainly analytical solutions, it is far from numerical techniques. This is a shortcoming of the book which, however, is not too important in spite of the large amount of material that it represents.

In contrast to the rather general title, the book is restricted to the above items. The part on the material theory, e.g., is quite short. In addition, some of the widespread errors in this field are also reproduced in this book. For example, the symmetry of the elasticity tensor with respect to the first two indices is definitely not a consequence of the symmetry of the stress tensor. The fourth rank identity maps all symmetric tensors into symmetric ones, without having the left subsymmetry. Moreover, any tensor with this subsymmetry is singular, and hence, a compliance tensor as an inverse of the stiffness tensor would not exist in this case.

As the book considers mainly analytical solutions, it is far from numerical techniques. This is a shortcoming of the book which, however, is not too important in spite of the large amount of material that it represents.

Reviewer: Albrecht Bertram (Magdeburg)

##### MSC:

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |

74B05 | Classical linear elasticity |

74E10 | Anisotropy in solid mechanics |