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Fracture propagation in brittle materials as a standard dissipative process: General theorems and crack tracking algorithms |
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| Affiliation: | 1. DICATAM, Università di Brescia, via Branze 43, 25123 Brescia, Italy;2. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, United States;3. Center for Shock Wave-processing of Advanced Reactive Materials, University of Notre Dame, Notre Dame, IN, United States;1. Institut Jean Le Rond d''Alembert (UMR 7190), UPMC-CNRS, Sorbonne Universités, F-75005 Paris, France;2. Laboratoire FAST, Univ. Paris-Sud, CNRS, Université Paris-Saclay, F-91405 Orsay, France;1. Institute of Engineering Thermophysics, Chinese Academy of Science, Beijing 100190, China;2. University of Chinese Academy of Science, Beijing 100049, China |
| Abstract: | The present work frames the problem of three-dimensional quasi-static crack propagation in brittle materials into the theory of standard dissipative processes. Variational formulations are stated. They characterize the three dimensional crack front “quasi-static velocity” as minimizer of constrained quadratic functionals. An implicit in time crack tracking algorithm that computationally handles the constraint via the penalty method algorithm is introduced and proof of concept is provided. |
| Keywords: | Brittle materials Crack growth Variational formulations Penalty method |
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