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Neural networks for computing in fracture mechanics. Methods and prospects of applications. (English) Zbl 0782.73077
Summary: A neural network is proposed and studied for the treatment of fracture mechanics problems. Both the cases of classical cracks and of cracks involving Coulomb’s friction or detachment (unilateral contact) interface conditions are considered. For the first case, the Hopfield model [J. J. Hopfield, Proc. Natl. Acad. Sci. 79, 2554-2558 (1982)] is appropriately modified, whereas for the second case, a neural model is proposed covering the case of inequalities. For this model, new results generalizing the results of J. J. Hopfield and D. W. Tank [Biol. Cybern. 52, 141-152 (1985; Zbl 0572.68041)] are obtained. Numerical applications illustrate the theory. Finally, the parameter identification problem for fractured bodies is formulated as a supervised learning problem.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74R99 Fracture and damage
92B20 Neural networks for/in biological studies, artificial life and related topics
68T05 Learning and adaptive systems in artificial intelligence
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