Book contents
- Frontmatter
- Contents
- Preface
- Foreword by Giulio Maier
- 1 Introduction
- 2 Elements of tensor algebra and analysis
- 3 Solid mechanics at finite strains
- 4 Isotropic non-linear hyperelasticity
- 5 Solutions of simple problems in finitely deformed non-linear elastic solids
- 6 Constitutive equations and anisotropic elasticity
- 7 Yield functions with emphasis on pressure sensitivity
- 8 Elastoplastic constitutive equations
- 9 Moving discontinuities and boundary value problems
- 10 Global conditions of uniqueness and stability
- 11 Local conditions for uniqueness and stability
- 12 Incremental bifurcation of elastic solids
- 13 Applications of local and global uniqueness and stability criteria to non-associative elastoplasticity
- 14 Wave propagation, stability and bifurcation
- 15 Post-critical behaviour and multiple shear band formation
- 16 A perturbative approach to material instability
- References
- Index
- Plate section
Preface
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Preface
- Foreword by Giulio Maier
- 1 Introduction
- 2 Elements of tensor algebra and analysis
- 3 Solid mechanics at finite strains
- 4 Isotropic non-linear hyperelasticity
- 5 Solutions of simple problems in finitely deformed non-linear elastic solids
- 6 Constitutive equations and anisotropic elasticity
- 7 Yield functions with emphasis on pressure sensitivity
- 8 Elastoplastic constitutive equations
- 9 Moving discontinuities and boundary value problems
- 10 Global conditions of uniqueness and stability
- 11 Local conditions for uniqueness and stability
- 12 Incremental bifurcation of elastic solids
- 13 Applications of local and global uniqueness and stability criteria to non-associative elastoplasticity
- 14 Wave propagation, stability and bifurcation
- 15 Post-critical behaviour and multiple shear band formation
- 16 A perturbative approach to material instability
- References
- Index
- Plate section
Summary
The purpose of this book is to present a research summary on solid mechanics at large strain, including the treatment of bifurcation and instability phenomena. The framework is crucial to the understanding of failure mechanisms in ductile materials, as connected to material instabilities, such as, shear banding.
I have employed Chapters 2 through 5 as a textbook for a graduate course on nonlinear elasticity that I have offered at the University of Trento since 1999, whereas Chapters 8, 10, 11 and 13 have been the basis for a course held at CISM (no. 414, ‘Material Instabilities in Elastic and Inelastic Solids’, H. Petryk, ed.). Chapters 6, 7, 9, 12, 14 and 15 have been added to present the elasticity and the yield critera in detail, including a treatment on elastic bifurcation and instability, wave propagation and multiple shear banding. This material has been taught during seminars for graduate students at various universities. Chapter 16 is devoted to the perturbative approach to material instability, developed by me in a series of articles in cooperation with D. Capuani, M. Brun, F. Dal Corso, M. Gei, A. Piccolroaz and J. R. Willis. Finally, I have to admit that the Introduction of the book is overlong; in fact, I have used it for a 20-hour graduate course on stability and bifurcation. The hope is to attract attention to the main topics presented in the book.
- Type
- Chapter
- Information
- Nonlinear Solid MechanicsBifurcation Theory and Material Instability, pp. xiii - xivPublisher: Cambridge University PressPrint publication year: 2012