Continuum theory of plasticity.

*(English)*Zbl 0856.73002
New York, NY: Wiley. x, 421 p. (1995).

If we distinguish between classical plasticity for small deformations and finite plasticity for large deformations, then to the best knowledge of the referent this is one of the first textbooks on finite plasticity. On one hand, this fact is quite surprising, as finite plasticity theory is needed in many applications, such as metal forming. And the pioneering papers in the field were written almost three decades ago. However, in reading the book, it is obvious that there is still a lack of a general theory which is based on clear physical assumptions and is put in a precise mathematical description. The authors cannot be blamed for this shortcoming, as it characterizes the state-of-the-art (and, yet, not of science). Many concepts have been suggested and are now widely used, without being substantiated by clear physical derivations. It is the merit of the authors, to be encouraged enough, to present the theory, as unsatisfying as it remains, without trying to hide this fact from the reader.

Before they enter into finite plasticity, the fundamental concepts of continuum mechanics are presented, as well as the classical theory of plasticity. The multiplicative and the additive decomposition approaches are treated, especially in the case of crystal plasticity. One would have expected more discussion on different approaches, including Mandel’s isoclinic configuration, e.g., or some remarks and comments on controversal concepts such as the plastic spin.

The notation is quite clear and consequent. However, many misprintings and mistakes (for example, confusing bold face for tensors with light face for scalars) reduce unfortunately the understanding and should be eliminated in the next edition, which will surely be needed for such an interesting and pioneering book.

Before they enter into finite plasticity, the fundamental concepts of continuum mechanics are presented, as well as the classical theory of plasticity. The multiplicative and the additive decomposition approaches are treated, especially in the case of crystal plasticity. One would have expected more discussion on different approaches, including Mandel’s isoclinic configuration, e.g., or some remarks and comments on controversal concepts such as the plastic spin.

The notation is quite clear and consequent. However, many misprintings and mistakes (for example, confusing bold face for tensors with light face for scalars) reduce unfortunately the understanding and should be eliminated in the next edition, which will surely be needed for such an interesting and pioneering book.

Reviewer: A.Bertram (Magdeburg)

##### MSC:

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

74C15 | Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) |

74C20 | Large-strain, rate-dependent theories of plasticity |