Conditions for contact/lack of contact along a loaded simple straight crack in plane isotropic elasticity
Loading...
Date
1997-03
Authors
Ioakimidis, Nikolaos
Journal Title
Journal ISSN
Volume Title
Publisher
Pergamon Press (Elsevier Science)
Abstract
The classical problem of a finite single straight crack inside an infinite plane isotropic elastic medium under a polynomial normal loading distribution along both crack edges is revisited. Here our intention is to derive a quantifier-free formula of general validity concerning the conditions for contact/lack of contact of the crack edges along the whole crack in terms of the loading parameters taking into consideration that the crack opening displacement should satisfy the physically posed inequality constraint that it must be a continuously positive quantity (in the popular case of no contact). Only if this restriction is satisfied, the classical elasticity solution (including the formulae for the stress intensity factors) actually holds true. The aforementioned task is achieved on the basis of classical algebraic approaches in the theory of polynomials including Sturm–Habicht sequences. The cases of polynomial loadings up to the quartic polynomial illustrate the present approach. Arbitrarily more general cases can also be considered by the Sturm–Habicht sequence method with the aid of appropriate computer software. Finally, an approximate approach related to general crack problems and hypersingular integral equations for their solution is also described in brief.