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
9 - Moving discontinuities and boundary value problems
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
Rules governing propagating and stationary discontinuity surfaces in solids are given in view of applications to shear banding and acceleration waves. The finite, rate and incremental boundary value problems are set for solids loaded by prescribed controlled nominal tractions on the boundary.
Analysis of kinematics and balance laws was given in Chapter 3, whereas constitutive equations were detailed in Chapters 4, 6 and 8, with a digression on yield functions presented in Chapter 7. We are now in a position to ‘collect the equations’ and set boundary value problems in finite and rate forms for solids loaded on the boundary. However, we have until now assumed certain hypotheses of regularity that we want to relax, so before setting boundary value problems, a digression on moving singularities in solids becomes instrumental. This also will be useful in the development of acceleration waves and shear band analysis.
Moving discontinuities in solids
Until now, we have more or less tacitly assumed that all the fields are ‘sufficiently’ regular, which is to say smooth. However, there are many situations in which smoothness or even continuity is lost. For instance, displacement, deformations or stresses can suffer jumps across a fracture or a so-called imperfect interface (such as those considered by Bigoni et al., 1997, 1998), or across a rigid thin inclusion (such as that considered by Dal Corso et al., 2008, and Dal Corso and Bigoni, 2009), or simply at an interface separating two different solids, for instance, in a multilaminated material.
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- Information
- Nonlinear Solid MechanicsBifurcation Theory and Material Instability, pp. 275 - 292Publisher: Cambridge University PressPrint publication year: 2012