Fundamentals of Plasticity in Geomechanics: 1st Edition (Hardback) book cover

Fundamentals of Plasticity in Geomechanics

1st Edition

By S. Pietruszczak

CRC Press

206 pages

Purchasing Options:$ = USD
Hardback: 9780415585163
pub: 2010-09-15

FREE Standard Shipping!


The book presents a concise, yet reasonably comprehensive, overview of fundamental notions of plasticity in relation to geomechanics. The primary objective of this work is to provide the reader with a general background in soil/rock plasticity and, as such, should be perceived as an introduction to the broad area of inelastic response of geomaterials.

The book is divided into eight chapters. Chapters 1 & 2 start with an outline of the basic concepts and fundamental postulates, followed by a review of the elastic-perfectly plastic formulations in geomechanics. The isotropic strain-hardening framework and isotropic-kinematic hardening rules, the latter formulated within the context of bounding surface plasticity, are discussed in Chapters 3 & 4. Chapter 5 outlines the basic techniques for numerical integration, whereas Chapter 6 gives an overview of procedures for limit analysis that include applications of lower and upper bound theorems. Both these chapters are introductory in nature and are intended to provide a basic background in the respective areas. Chapter 7 deals with description of inherent anisotropy in geomaterials. Finally, Chapter 8 provides an overview of the experimental response of geomaterials.

The text is intended primarily for Ph.D./M.Sc. students as well as researchers working in the areas of soil/rock mechanics. It may also be of interest to practicing engineers familiar with established notions of contemporary continuum mechanics.

Table of Contents



Chapter 1. Basic concepts of the theory of plasticity

1.1 Typical approximations of uniaxial response of the material

1.2 The notion of generalized yield/failure criterion

1.3 Generalization of the concept of elastic-perfectly plastic and strain hardening material

1.4 Determination of plastic strain; deformation and flow theories of plasticity

1.5 Review of fundamental postulates of plasticity; uniqueness of the solution

Chapter 2. Elastic-perfectly plastic formulations in geomechanics

2.1 General considerations

2.2 Geometric representation of the failure surface

2.3 Selection of stress invariants for the mathematical description

2.4 Typical failure criteria for geomaterials

2.4.1 Mohr-Coulomb failure criterion

2.4.2 Drucker-Prager and other derivative criteria

2.4.3 Modified criteria based on smooth approximations to Mohr-Coulomb envelope

2.4.4 Non-linear approximations in meridional section

2.5 Derivation of constitutive relation

2.5.1 Matrix formulation

2.6 Consequences of a non-associated flow rule

Chapter 3. Isotropic strain-hardening formulations

3.1 ‘Triaxial’ tests and their mathematical representation

3.1.1 Mohr-Coulomb criterion in ‘triaxial’ space

3.1.2 On the behaviour of a perfectly plastic Mohr-Coulomb material

3.1.3 Review of typical mechanical characteristics of granular materials

3.2 Volumetric hardening; Critical State model

3.2.1 Formulation in the ‘triaxial’ {p,q} space

3.2.2 Comments on the performance

3.2.3 Generalization and specification of the constitutive matrix

3.3 Deviatoric hardening model

3.3.1 Formulation in the ‘triaxial’ {p,q} space

3.3.2 Comments on the performance

3.3.3 Generalization and specification of the constitutive matrix

3.4 Combined volumetric-deviatoric hardening

3.5 Specification of constitutive matrix under undrained conditions 

Chapter 4. Combined isotropic-kinematic hardening rules

4.1 Bounding surface plasticicty; volumetric hardening framework

4.1.1 Formulation in the ‘triaxial’ {p,q} space

4.1.2 Comments on the performance

4.1.3 Generalization and specification of the constitutive matrix

4.2 Bounding surface plasticicty; deviatoric hardening framework

4.2.1 Formulation in the ‘triaxial’ {P,Q} space

4.2.2 Comments on the performance

4.2.3 Generalization and specification of the constitutive matrix

Chapter 5. Numerical integration of constitutive relations

5.1 Euler’s integration schemes

5.2 Numerical integration of {p,q} formulation

5.2.1 Stress-controlled scheme

5.2.2 Strain-controlled schemes

5.3 Numerical examples of integration in {p,q}-space

5.3.1 Critical State model; drained p=const. compression

5.3.2 Deviatoric hardening model; drained ‘triaxial’ compression

5.3.3 Deviatoric hardening model; undrained ‘triaxial’ compression

5.4 General methods for numerical integration

5.4.1 Statement of algorithmic problem

5.4.2 Notion of closest point projection

5.4.3 Return-mapping algorithms

Chapter 6. Introduction to limit analysis

6.1 Formulation of lower and upper bound theorems

6.2 Examples for applications of limit theorems in geotechnical engineering

Chapter 7. Description of inherent anisotropy in geomaterials

7.1 Formulation of anisotropic failure criteria

7.1.1 Specification of failure criteria based on critical plane approach

7.1.2 Formulation of failure criteria incorporating a microstructure tensor

7.2 Description of inelastic deformation process

7.2.1 Plasticity formulation for critical plane approach

7.2.2 Plasticity formulation incorporating a microstructure tensor

7.2.3 Numerical examples

Chapter 8. Experimental trends in the mechanical behaviour of soils and rocks

8.1 Basic mechanical characteristics in monotonic tests under drained conditions

8.1.1 Influence of confining pressure; compaction/dilatancy

8.1.2 Influence of Lode’s angle and the phenomenon of strain localization

8.2 Undrained response of granular media; pore pressure evolution, liquefaction

8.3 Basic mechanical characteristics in cyclic tests; hysteresis and liquefaction

8.4 Inherent anisotropy; strength characteristics of sedimentary rocks

8.5 Identification of basic material parameters for soils/rocks

8.5.1 General remarks on identification procedure

8.5.2 Examples involving deviatoric hardening framework


Appendix: Suggested exercises

About the Author

Dr. Stan Pietruszczak is professor of Civil Engineering at McMaster University in Canada. His research interests are in the following areas:

Geotechnical Engineering: Modelling of mechanical response of geomaterials (soils, rocks, etc) to both monotonic and fluctuating loads. Description of inherent and induced anisotropy through incorporation of some tensorial functions reflecting the evolution of material microstructure. Modelling of the chemo-mechanical interaction in rocks / soils. Description of strain localization phenomenon, in dry and saturated soils, through a homogenization technique.

Structural Mechanics: Numerical analysis of concrete structures, including nuclear containment structures. Assessment of seismic stability of masonry structures. Modelling of the mechanical effects of alkali-aggregate reaction in hydraulic structures. Description of the response of saturated cemented aggregate mixtures, including localized deformation.

Biomechanics: Description of aging and functional adaptation of bone. Evaluation of risk of fracture of bones; modelling of bone-implant interaction.

He has published over 140 refereed papers.

Subject Categories

BISAC Subject Codes/Headings: