Advances in Applied Mechanics

6.5 Cracks in terms of stratified curvature varifolds

If a two-dimensional crack appears in the deformed configuration ${\mathcal{B}}_{\text{a}}:=u\left(\mathcal{B}\right)$ and crosses a generic point $u\left(x\right),x\in \mathcal{B}$, its “direction” is locally described by the tangent plane to the crack at u (x), when the crack is smooth. When the crack margins have a corner at u (x), a cone of planes has to be considered. Crack patterns can, however, be very irregular. We could accept a set as a representative of a crack pattern when it is just rectifiable, as mentioned before, for we should have at our disposal ...