5R1. Constitutive Modelling of Geomaterials. - B Cambou (Laboratoire de Tribologie et Dynamique des Syst, Ecole Centrale de Lyon, 36 Ave Guy de Collongue, Ecully Cedex, 69131, France) and C Di Prisco (Politecnico di Milano, Piazza Leonardo da Vinci 32, Milan, 20133, Italy). Hermes Sci Publ, Paris. 2000. 233 pp. Softcover. ISBN 1-903398-06-1. $74.95.

Reviewed by K Hutter (Dept of Mech, Darmstadt Univ of Tech, Hochschulstr 1, Darmstadt, D-64289, Germany).

This monograph consists of seven lectures, written by nine specialists of geotechnique, emphasizing their fields of interest and thought as an advanced course to engineering students at the graduate level. The lectures are consecutively arranged and hinge upon one another, but are equally independently readable each with its own reference list. Cross references are loose, and no index is provided.

Apart from an editorial (F Darve), Chapter 1 (R Chambon) provides a “General presentation of constitutive modeling of geomaterials” on the basis of continuum mechanics and geared to the application of the finite element method. The lecture browses through the principle of virtual power; touches many material peculiarities such as cyclic, viscous and relaxation effects, localization, and rupture; culminates in Section 4 in the well-known terminology of the Nonlinear Field Theories of Mechanics by Truesdell and Noll; and terminates in stating well posedness (in the sense of Hadamand). The presentation is colloquial, shallow in depth with occasional slips in the English language, perhaps useful as a source of references.

Chapter 2 on “Continuum damage modeling” (G Pijandier-Cabot) is restricted to elasto-plasticity and its change of properties under microstructural degradation. First, elasto-plastic damage and crack closure effects are described; then an internal length is incorporated providing a failure model that is consistent with fracture mechanics and paving the route to induced anisotropic behavior. Finally, environmentally-induced damage effects are discussed. The concepts are simply and clearly introduced, and the scope is limited to the description of damage phenomena in concrete.

Chapter 3 provides an introduction into “Incrementally nonlinear modeling” (F Darve and X Roguiez), a subject pioneered by the principal author. The key idea is to express the strain increment as a function of the stress increment in a rate independent fashion or vice versa. For a quadratic dependence of the strain increment upon the stress increment, elasto-plastic tangent moduli are constitutively prescribed for which two formulations having only five phenomenological parameters are presented. These are determined with typical oedometric tests, and the final model is then applied under uniaxial extension and compression to study questions of material instability. The text is brief and assumes detailed advanced knowledge of the reader.

Chapter 4 presents a comprehensive introduction into the “Elements of hypoplasticity” (D Kolymbas). The author carefully introduces notions such as elasticity, elasto-plasticity, and hypoelasticity and cul-minates in the presentation of the general form of a hypoplastic constitutive model as an equation relating the Jaumann stress rate as a nonlinear functional of the stress and stretching. It is shown that this functional needs to be nonlinear and rate independent in the stretching to capture typical soil behavior. A particular formula is shown, and questions of parameter identifications are touched. The author also addresses points of weaknesses that have so far been observed with hypo-plastic constitutive relations and gives a review of proposed hypoplastic equations. The chapter is thoughtfully written and adequate for students to learn the subject.

“Constitutive equations in plasticity” (C die Pricso and M Pastor), in Chapter 5, provides a comprehensive account of elastoplastic constitutive modeling with yield surface from a theoretical as well as experi-mental point of view. Perfect plasticity with Tresca, Mises, and Mohr-Coulomb failure surfaces and single potential hardening plasticity are discussed as is (induced) anisotropy. The concepts of cyclic loading, kinematic hardening densification, and liquefaction of sand are equally touched upon. Further sections are devoted to viscoplasticity and damage and instability in load-controlled tests—a subject still under intensive debate. The chapter is long (57 pages), well written and attempts to provide a balanced review, but unfortunately does not give an abstract.

The scope and spirit of Chapter 6, on “Higher order constitutive models” (I Vardoulakis), is somewhat different from the remaining contributions as it is the only one using higher-order gradient models. By way of illustration, second gradient theories account for local curvature effects; so an internal length scale is naturally introduced. Using beams as an illustration, the author then presents Mindlin’s 2nd gradient linear elasticity theory before he introduces the gradient plasticity model for granular materials. These formulations necessarily require the introduction of surface double forces which are carefully introduced. It is further demonstrated that shear band localization and cavity collapse can naturally be described with such formulations and that the boundary layer thicknesses are directly connected to the internal length scale.

Chapter 7 deals with “Constitutive modeling of granular materials from a change of scale” (B Cambou). Its subject is homogenization, ie, the transfer of the properties of the grains and their interaction to the macroscale of which a typical length is several grain diameters. By way of introducing local variables such as void ratio, coordination number (ie, average number of contacts per particle) fabric tensors, and applying rules defining the macroscopic stress tensor in terms of contact forces and contact orientations, macroscopic stress relations can be derived, provided that rules are also given which define the macroscopic kinematics in terms of the microscopic deformations. Several models are presented, and their performance is covered briefly. The presentation is brief, but clear and provides an acceptable introduction into quasistatic (mostly) linear behavior.

As for the printing, the book could have been more carefully edited. There is much better software available in which formulas appear in better form. Figures have varied style and inset texts are often hardly readable; equally, captions are often insufficient. Whereas all authors write in acceptable English, a more careful devotion to the text by the copy editor would have eliminated occasional slips and unified the style. As a whole, Constitutive Modelling of Geomaterials is useful for upper-level students and researchers to obtain an impression about present day constitutive modeling of geomaterials with a fairly extensive reference list.