Villaggio, Piero Detachment instabilities in membranes. (English) Zbl 0547.73089 Meccanica 19, 201-205 (1984). Summary: Some free boundary value problems involving the equilibrium of elastic membranes are examined. Each membrane is clamped along a part of the boundary and uniformly loaded along another part. The clamped part is weakened by a crack. As the exterior load increases, the crack tends to extend and, for a certain critical value of the load, may run catastrophically. Cited in 1 Document MSC: 74R99 Fracture and damage 74K15 Membranes 74R05 Brittle damage 35R35 Free boundary problems for PDEs Keywords:free boundary value problems; equilibrium of elastic membranes; clamped along a part of the boundary; uniformly loaded along another part; weakened by a crack PDFBibTeX XMLCite \textit{P. Villaggio}, Meccanica 19, 201--205 (1984; Zbl 0547.73089) Full Text: DOI References: [1] Rivlin R.S.,The Effective Work of Adhesion, Paint Technology, Vol. IX, N.106, 1–4 (1944). [2] Knopoff L., Mouton J.O., Burridge R.,The Dynamics of a One-Dimensional Fault in the Presence of Friction, Geophys. J.R. Astr. Soc., 35, 169–184 (1973). [3] Burridge R. andKeller J.B.,Peeling, Slipping and Cracking-Some One-Dimensional Free Boundary Problems in Mechanics, SIAM Rew. Vol. 20, N. 1, 31–61 (1978). · Zbl 0394.73093 · doi:10.1137/1020003 [4] Weinberger H.F.,Partial Differential Equations (A First Course), Waltham: Blaisdell (1965). · Zbl 0127.04805 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.