Plasticity for structural engineers.

*(English)*Zbl 0666.73010
New York etc: Springer-Verlag. xiii, 606 p. DM 128.00 (1988).

Although the authors intended this book primarily for structural engineers familiar with the process of elastic and plastic analysis, it is surely recommendable for the one who wants to learn about the basic concepts of plasticity as well, which are carefully described. Moreover, as very many (solved) problems are included, this is an appropriate textbook for self-studies as well as for student courses.

After some general comments on history, notation, etc. the authors start with the description of yield and failure criteria. The elastic theory (linear and nonlinear), as the basis for elastic-plastic models, is shortly outlined, followed by the topics of classical plasticity such as plastic potentials, associated flow rules, convexity, normality, uniqueness, the \(J_ 2\) theory, hardening, and Drucker’s postulate.

Then we can find two long chapters on metal and concrete plasticity. Surprisingly, we find a lot of information about numerical techniques such as the finite-element-method. Up to now, it is not standard in this kind of books, that the numerical treatment of the resulting problems not solvable analytically, is given. The reader will surely be thankfull about this exception, because computational methods can hardly be separated from the problems they are meant to solve. The last part deals on limit analysis. The general theory is given as well as applications to beams, frames, plates and shells.

Two small critical comments shall be given in this place. Firstly, Cauchy elasticity does not violate the laws of thermodynamics. Only for very special cases such as isothermal or isentropic processes a potential law (Green elasticity) can be deduced from thermodynamics [see C. C. Wang and C. Truesdell, Introduction to rational elasticity. (1973; Zbl 0308.73001); p. 193]. Secondly, the stability consideration are all given under the label “Drucker”, even in the non plastic context. Despite of the great merits of D. C. Drucker, infinitesimal stability is connected with the names of Hadamard, Duhem and others since the beginning of this century.

But apart from these comments, the book as a whole is surely recommendable for all who want to know more about plasticity.

After some general comments on history, notation, etc. the authors start with the description of yield and failure criteria. The elastic theory (linear and nonlinear), as the basis for elastic-plastic models, is shortly outlined, followed by the topics of classical plasticity such as plastic potentials, associated flow rules, convexity, normality, uniqueness, the \(J_ 2\) theory, hardening, and Drucker’s postulate.

Then we can find two long chapters on metal and concrete plasticity. Surprisingly, we find a lot of information about numerical techniques such as the finite-element-method. Up to now, it is not standard in this kind of books, that the numerical treatment of the resulting problems not solvable analytically, is given. The reader will surely be thankfull about this exception, because computational methods can hardly be separated from the problems they are meant to solve. The last part deals on limit analysis. The general theory is given as well as applications to beams, frames, plates and shells.

Two small critical comments shall be given in this place. Firstly, Cauchy elasticity does not violate the laws of thermodynamics. Only for very special cases such as isothermal or isentropic processes a potential law (Green elasticity) can be deduced from thermodynamics [see C. C. Wang and C. Truesdell, Introduction to rational elasticity. (1973; Zbl 0308.73001); p. 193]. Secondly, the stability consideration are all given under the label “Drucker”, even in the non plastic context. Despite of the great merits of D. C. Drucker, infinitesimal stability is connected with the names of Hadamard, Duhem and others since the beginning of this century.

But apart from these comments, the book as a whole is surely recommendable for all who want to know more about plasticity.

Reviewer: A.Bertram

##### MSC:

74Cxx | Plastic materials, materials of stress-rate and internal-variable type |

74-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids |

74C99 | Plastic materials, materials of stress-rate and internal-variable type |

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

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

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74R20 | Anelastic fracture and damage |