On the cracking patterns of brittle rings with elastic radial support under hydrostatic pressure

Abstract

AbstractThe evolution of the cracking pattern of an internally pressurized, circular, brittle ring supported with radial elastic springs is investigated. The ill-posed Griffith-type energy functional is regularized via a sequence of boundary value problems (BVPs). We show, that internal bending in the fragments plays an essential role in the position of the new crack. We also find that the pattern formation is driven by a co-dimension one bifurcation, which leads to the conclusion that in the beginning of the cracking process the new crack emerges in the vicinity of the existing cracks. In the second phase of the evolution the cracking process obeys a halving rule. The critical value of the fragment-length is derived. The results obtained are readily applicable to describe the crack evolution of hemispherical domes.