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  • Print publication year: 2012
  • Online publication date: August 2012

9 - Moving discontinuities and boundary value problems

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.