By J.F. Labuz, A. Drescher
This ebook includes a sampling of papers provided on the June 2-5, 2002 overseas Workshop on Bifurcations andamp; Instabilities in Geomechanics (IWBI 2002). The scope of the Workshop comprises analytical methods, numerical tools, and experimental options.
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Additional info for Bifurcations and Instabilities in Geomechanics: Proceedings of the International Workshop, IWBI 2002, Minneapolis, Minnesota, 2-5 June 2002
D. 1995. Experimental determination of probability distributions for parameters of a salem limestone cap plasticity model. Mech. Mat. 21:119-137. Fossum, A. F. & Fredrich, J. T. 2000. Cap plasticity models and compactive and dilatant pre-failure deformations. In J. Girard, M. Liebman, C. Breeds, & T. ), Pacific Rocks 2000: 1169-1176. Rotterdam: Balkema. Gu, C, Kim, M. & Anand, L. 2001. Constitutive equations for metal powders: application to powder forming processes. Int. J. Plasticity 17: 147-209.
Suggestion for implementation into a computer program is also proposed. It is known from the theory of partial differential equations, that the solution of a differential equation system is not uniquely determined by the equation system itself, so therefore one has properly to formulate initial and boundary conditions, which completely determine a solution of the differential equation system. However, apart from this there is still another supplementary consideration to be worked out, which plays an important role especially in numerics.
For the considered rupture mode, this is the path with maximum positive KI or, equivalently (Erdogan & Sih 1963, Cotterell & Rice 1980), with zero KII. Hence, on the macroscopic level, we have the condition defining the external load: (10) and the condition defining the direction of the crack propagation: (11) In particular cases there may be a number of rays for which the tensile stress in the FPZ σθθ has local maximum. The preferable one is that with maximum value of . Macroscopically, this microscopic bifurcation may appear as bifurcation of the crack trajectory: the latter chooses the direction corresponding to the greatest KI.
Bifurcations and Instabilities in Geomechanics: Proceedings of the International Workshop, IWBI 2002, Minneapolis, Minnesota, 2-5 June 2002 by J.F. Labuz, A. Drescher