Motions

Abstract

Motions y are defined as in Section 2a, except that y is not required to be continuous across the crack. Precisely, y (X, t) is assumed to be smooth away from the tip, to satisfy the impenetrability condition

$$ [y] \cdot m \geqslant 0, $$

(26-1)

and to have a limiting value y(Z(t), t) at the tip,

$$ y(X,t) \to y(Z(t),t) as X \to Z(t) $$

(26-2)

from bulk or from points of the crack, so that the deformed tip is well defined. The deformation gradient F = ∇y and the material velocity $\dot y$ are then smooth away from the tip, although these fields are generally singular at the tip.