Complete damage in elastic and viscoelastic media and its energetics |
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| Authors: | Alexander Mielke Tomáš Roubíček Jan Zeman |
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| Affiliation: | 1. Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, D-10117 Berlin, Germany;2. Institut für Mathematik, Humboldt Universität zu Berlin, Rudower Chaussee 25, D-12489 Berlin, Germany;3. Mathematical Institute, Charles University, Sokolovská 83, CZ-186 75, Praha 8, Czech Republic;4. Institute of Thermomechanics of the ASCR, Dolej?kova 5, CZ-182 00, Praha 8, Czech Republic;5. Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, CZ-166 29, Praha 6, Czech Republic;1. Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, ul. prof. S. ?ojasiewicza 6, 30-348 Kraków, Poland;2. University of Warsaw, Mathematics Department, ul.Banacha 2, 02-957 Warsaw, Poland;1. Institute for Structure Mechanics, Bauhaus University Weimar, Marienstr. 15, Weimar 99423, Germany;2. School of Civil Engineering of Barcelona (ETSECCPB), Departament de Matemática Aplicada 3, Universitat Politècnica de Catalunya, Spain;3. Laboratori de Càlcul Numèric, Universitat Politècnica de Catalunya (UPC Barcelona-Tech), 08034 Barcelona, Spain;4. Professor School of Civil, Environmental and Architectural Engineering, Korea University, Republic of Korea;1. National Engineering Research Center for Coal & Gas Control, Faculty of Safety Engineering, China University of Mining & Technology, Xuzhou 221116, China;2. State Key Laboratory of Coal Resources and Mine Safety, China University of Mining and Technology, Xuzhou 221116, China;3. Key Laboratory of Gas and Fire Control for Coal Mine, Faculty of Safety Engineering, China University of Mining & Technology, Xuzhou 221116, China;1. School of Mechanical and Mining Engineering, The University of Queensland, QLD 4072, Australia;2. State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Jiangsu 221116, China;3. CSIRO Energy Flagship, Clayton South 3169, Australia |
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| Abstract: | A model for the evolution of damage that allows for complete disintegration is addressed. Small strains and a linear response function are assumed. The “flow rule” for the damage parameter is rate-independent. The stored energy involves the gradient of the damage variable, which determines an internal length-scale. Quasistatic fully rate-independent evolution is considered as well as rate-dependent evolution including viscous/inertial effects. Illustrative 2-dimensional computer simulations are presented, too. |
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