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**Plasticity. A treatise on finite deformation of heterogeneous inelastic materials.**
*(English)*
Zbl 1073.74001

Cambridge Monographs on Mechanics. Cambridge: Cambridge University Press (ISBN 0-521-83979-3). xxv, 730 p. (2004).

Providing a basic foundation for advanced graduate study and research in the mechanics of solids, this treatise contains a systematic development of the fundamentals of finite inelastic deformations of heterogeneous materials. The book combines the mathematical rigor of solid mechanics with the physics-based micro-structural understanding of materials science, to present a coherent picture of finite inelastic deformation of single- and poly-crystal metals over broad ranges of strain rates and temperatures. It also includes a similarly rigorous and experimentally based development of the quasi-static deformation of cohesionless granular materials that support the applied loads through contact friction. Every effort is made to provide a thorough treatment of the subject, rendering the book accessible to students in solid mechanics and in mechanics of materials. This is the only book that seamlessly integrates rigorous mathematical description of finite deformations with mechanisms-based micromechanics to produce useful results with relevance to practical problems.

As a foundation, the geometrical, kinematical, and dynamical ingredients are treated in Chapters 1–3: Geometry; Kinematics; Stress and stress-rate measures, and balance relations. For the most part, coordinate-independent vector and tensor notation is used. This however, is augmented by frequent component representation of various expressions in indicial notation, rendering the book accessible to a broader audience. The continuum theories of the rate-independent and rate-dependent deformation of metals and geomaterials (granular materials and rocks) are developed in Ch. 4, Continuum theories of elastoplasticity, where, based on a general framework, many specific cases are detailed, and explicit equations useful for computational simulations are given. Detailed presentations of dislocation-based rate- and temperature-dependent models of metals, together with experimentally-obtained values of the corresponding constitutive parameters are included in this chapter. In Ch. 5, Integration of continuum constitutive equations, both rate-independent and rate-dependent deformations, including the effects of thermal softening, friction, and dilatancy, are considered. Included are forward-gradient integration techniques, as well as a more efficient technique based on a plastic-predictor/elastic-corrector method, recently developed by the author and his coworkers. Each computational method is described, computational steps are listed, and illustrative examples are provided, leading to a comparative evaluation of various methods.

Ch. 6, Finite elastoplastic deformation of single crystals, contains the fundamentals of finite elastoplastic deformation of single crystals, from a micromechanical point of view, starting with a review of the crystal systems and certain elementary topics in the theory of dislocations. Physically-based constitutive relations for single crystals are formulated in this chapter on the basis of slip-induced plastic deformation and the accompanying elastic lattice distortion. The notions of self- and latent-hardening are critically examined, and slip models which directly account for both the temperature- and strain-rate effects, are presented and applied to predict the polycrystal flow stress of both bcc (commercially pure tantalum) and fcc (OFHC copper) metals over a broad range of strains, strain rates, and temperatures. Ch. 7, Finite plastic deformation of granular materials, covers the micromechanics of finite elastoplastic deformation of densely packed granular materials. Here, physically-based constitutive relations are developed for particulate materials that carry the applied loads through frictional contacts, based on the slip- and rolling-induced (anisotropic) inelastic deformation, accompanied by shear-induced and pressure-dependent inelastic volumetric changes. In Ch. 8, Average quantities and homogenization models, the mathematical foundation of the transition from micro- to macro-variables is laid out. Exact results on averaging techniques, valid at finite deformations and rotations, are developed, giving explicit equations for the calculation of the generalized Eshelby tensor and its conjugate, within a nonlinear finite-deformation setting. Aggregate properties and averaging models are presented in this chapter, including the Taylor, the self-consistent, and the double-inclusion models.

Special advanced experimental methods are reviewed in Ch. 9, Special experimental techniques, and some typical experimental results on large strain, high strain-rate deformation of several metals are given. Included also are experimental results on the deformation and shear banding of cohesionless frictional granular materials.

As a foundation, the geometrical, kinematical, and dynamical ingredients are treated in Chapters 1–3: Geometry; Kinematics; Stress and stress-rate measures, and balance relations. For the most part, coordinate-independent vector and tensor notation is used. This however, is augmented by frequent component representation of various expressions in indicial notation, rendering the book accessible to a broader audience. The continuum theories of the rate-independent and rate-dependent deformation of metals and geomaterials (granular materials and rocks) are developed in Ch. 4, Continuum theories of elastoplasticity, where, based on a general framework, many specific cases are detailed, and explicit equations useful for computational simulations are given. Detailed presentations of dislocation-based rate- and temperature-dependent models of metals, together with experimentally-obtained values of the corresponding constitutive parameters are included in this chapter. In Ch. 5, Integration of continuum constitutive equations, both rate-independent and rate-dependent deformations, including the effects of thermal softening, friction, and dilatancy, are considered. Included are forward-gradient integration techniques, as well as a more efficient technique based on a plastic-predictor/elastic-corrector method, recently developed by the author and his coworkers. Each computational method is described, computational steps are listed, and illustrative examples are provided, leading to a comparative evaluation of various methods.

Ch. 6, Finite elastoplastic deformation of single crystals, contains the fundamentals of finite elastoplastic deformation of single crystals, from a micromechanical point of view, starting with a review of the crystal systems and certain elementary topics in the theory of dislocations. Physically-based constitutive relations for single crystals are formulated in this chapter on the basis of slip-induced plastic deformation and the accompanying elastic lattice distortion. The notions of self- and latent-hardening are critically examined, and slip models which directly account for both the temperature- and strain-rate effects, are presented and applied to predict the polycrystal flow stress of both bcc (commercially pure tantalum) and fcc (OFHC copper) metals over a broad range of strains, strain rates, and temperatures. Ch. 7, Finite plastic deformation of granular materials, covers the micromechanics of finite elastoplastic deformation of densely packed granular materials. Here, physically-based constitutive relations are developed for particulate materials that carry the applied loads through frictional contacts, based on the slip- and rolling-induced (anisotropic) inelastic deformation, accompanied by shear-induced and pressure-dependent inelastic volumetric changes. In Ch. 8, Average quantities and homogenization models, the mathematical foundation of the transition from micro- to macro-variables is laid out. Exact results on averaging techniques, valid at finite deformations and rotations, are developed, giving explicit equations for the calculation of the generalized Eshelby tensor and its conjugate, within a nonlinear finite-deformation setting. Aggregate properties and averaging models are presented in this chapter, including the Taylor, the self-consistent, and the double-inclusion models.

Special advanced experimental methods are reviewed in Ch. 9, Special experimental techniques, and some typical experimental results on large strain, high strain-rate deformation of several metals are given. Included also are experimental results on the deformation and shear banding of cohesionless frictional granular materials.

Reviewer: Anatoliy S. Semenov (Odessa)

### 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 |

74E20 | Granularity |

74E05 | Inhomogeneity in solid mechanics |