Book contents
- Frontmatter
- Contents
- Preface
- Historical perspective
- Notation
- 1 Introduction to plasticity: experimental facts
- 2 Thermomechanics of elastoviscoplastic continua
- 3 Small-strain elastoplasticity
- 4 Problems in perfect elastoplasticity
- 5 Elastoplasticity with strain-hardening
- 6 Elements of limit analysis
- 7 Crack propagation and fracture mechanics
- 8 Elastoplasticity with finite strains
- 9 Homogenization of elastoplastic composites
- 10 Coupling between plasticity and damage
- 11 Numerical solution of plasticity problems
- 12 Experimental study using infrared thermography
- Appendix 1 Thermodynamics of continuous media
- Appendix 2 Convexity
- Appendix 3 Analytic solutions of some problems in elastoplasticity
- Appendix 4 Analytic computation of stress-intensity factors
- Further reading
- Bibliography
- Index
Appendix 3 - Analytic solutions of some problems in elastoplasticity
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Historical perspective
- Notation
- 1 Introduction to plasticity: experimental facts
- 2 Thermomechanics of elastoviscoplastic continua
- 3 Small-strain elastoplasticity
- 4 Problems in perfect elastoplasticity
- 5 Elastoplasticity with strain-hardening
- 6 Elements of limit analysis
- 7 Crack propagation and fracture mechanics
- 8 Elastoplasticity with finite strains
- 9 Homogenization of elastoplastic composites
- 10 Coupling between plasticity and damage
- 11 Numerical solution of plasticity problems
- 12 Experimental study using infrared thermography
- Appendix 1 Thermodynamics of continuous media
- Appendix 2 Convexity
- Appendix 3 Analytic solutions of some problems in elastoplasticity
- Appendix 4 Analytic computation of stress-intensity factors
- Further reading
- Bibliography
- Index
Summary
The object of the appendix It is clear that elastoplasticity problems are not easily amenable to analytical methods, but for a few exceptions as in the case of the spherical envelope in Chapter 6. In particular, the elastoplastic borderline separating the region where the material still behaves elastically and the already plasticized region is an unknown in such problems. For complex geometries then a numerical implementation seems necessary (Chapter 11). However, the few cases that admit analytical solutions are typical of a methodology of which any student and practitioner of elastoplasticity must be aware. We have thus selected four examples, the first in plane strain (the wedge problem), the second in torsion, the third exhibiting a complex loading and the fourth accounting for anisotropy in a composite material.
Elastoplastic loading of a wedge
General equations
A wedge of angle β < π/2 is made of an isotropic elastoplastic material, satisfying Hooke's law in the elastic regime and Tresca's criterion without hardening at the yield limit. On its upper face it is subjected to a pressure p which increases with time (Fig. A3.1). We look first for the fully elastic solution and then for the elastoplastic solution in which the plasticized zone progresses until the whole wedge has become plastic. The solution of this problem in the elastoplastic framework is due to Naghdi (1957) – see also Murch and Naghdi (1958) and Calcotte (1968, pp. 158–64).
- Type
- Chapter
- Information
- The Thermomechanics of Plasticity and Fracture , pp. 293 - 312Publisher: Cambridge University PressPrint publication year: 1992