TY - JOUR
T1 - Unstable growth of tension cracks in brittle solids
T2 - Stable and unstable bifurcations, snap-through, and imperfection sensitivity
AU - Nemat-Nasser, S.
AU - Sum, Y.
AU - Keer, L. M.
N1 - Funding Information:
Acknowledgements-This work was supported by the National Science Foundation under Grant ENG 77-22155 and by the Los Alamos Scientific Laboratory, University of California, under contract P.O. No. N68-8539G-1 to Northwestern University.
PY - 1980
Y1 - 1980
N2 - The growth pattern of a system of tension cracks in a linearly elastic brittle solid, may undergo abrupt changes, e.g. some cracks may stop or actually close, as others snap to finitely longer lengths. For the growth regime of a system of straight edge cracks in plane strain, the concepts of fundamental equilibrium path, stable and unstable bifurcation points and snap-through critical point are introduced and the corresponding behaviors are studied. In particular, it is shown that instabilities of this kind are highly imperfection-sensitive in the sense that, for example, a small material inhomogeneity can decrease by a large amount the critical value of the load parameter at which a growth regime abruptly changes to a new one. For thermally induced tension edge cracks in an infinite strip of finite width, numerical results are presented and various aspects of the theory are illustrated. For the calculation the new combined analytic and finite-element solution method recently given by the authors is employed.
AB - The growth pattern of a system of tension cracks in a linearly elastic brittle solid, may undergo abrupt changes, e.g. some cracks may stop or actually close, as others snap to finitely longer lengths. For the growth regime of a system of straight edge cracks in plane strain, the concepts of fundamental equilibrium path, stable and unstable bifurcation points and snap-through critical point are introduced and the corresponding behaviors are studied. In particular, it is shown that instabilities of this kind are highly imperfection-sensitive in the sense that, for example, a small material inhomogeneity can decrease by a large amount the critical value of the load parameter at which a growth regime abruptly changes to a new one. For thermally induced tension edge cracks in an infinite strip of finite width, numerical results are presented and various aspects of the theory are illustrated. For the calculation the new combined analytic and finite-element solution method recently given by the authors is employed.
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U2 - 10.1016/0020-7683(80)90102-X
DO - 10.1016/0020-7683(80)90102-X
M3 - Article
AN - SCOPUS:0019146383
VL - 16
SP - 1017
EP - 1035
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
SN - 0020-7683
IS - 11
ER -