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Mesoscopic theory of microcracks

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The mesoscopic concept is a way to deal with complex materials with an internal structure within continuum mechanics. It consists of extending the domain of the balance equations by mesoscopic variables and of introducing a local distribution function of these variables as a statistical element. In our case microcracks are modelled as penny-shaped and are completely characterized by their diameter and the unit normal to the crack surface. Two examples of crack dynamics are given as well as a possible definition of a damage parameter. Orientational order parameters (fabric-alignment tensors) are defined and balance-like dynamic equations for them are derived.
Rocznik
Strony
481--499
Opis fizyczny
Bibliogr. 34 poz.
Twórcy
autor
  • Technische Universitat Berlin, Institut fur Mechanik, Strasse des 17. Juni 10623 Berlin
autor
  • Budapest University of Technology and Economics Department of Chemical Physics 1521 Budapest
autor
  • Technische Universitiit Berlin Institut fur Theoretische Physik Hardenbergstr. 36 10623 Berlin
Bibliografia
  • 1. W. MUSCHIK, Internal variables in non-equilibrium thermodynamics, J . Non-Equilib. Thermodyn., 15, 1990.
  • 2. G. A. MAUGIN and W. MUSCHIK, Thermodynamics with internal variables, J. Non Equilib. Thermodyn., 19, 1994.
  • 3. L. M. KACHANOV, On the time to failure under creep conditions, Izv. AN SSSR, Otd. Tekhn. Nauk., 8, 1958.
  • 4. G. A. MAUGIN, The Thermomechanics of Plasticity and Fracture, Chap. 7, Cambridge University Press, Cambridge 1992.
  • 5. D. KRAJCINOVIC, Damage mechanics, Elsevier, Amsterdam, etc., 1996.
  • 6. K. I. KANATANI, Distribution of directional data and fabric tensors, International Journal of Engineering Science, 22, 2, 149- 164, 1984.
  • 7. J. L. ERICKSEN, Anisotropic fluids, Arch. Rat. Mech. Anal., 4,1960.
  • 8. F. J. LESLIE, Some constitutive equations for liquid crystals, Arch. Rat. Mech. Anal., 28, 1965.
  • 9. S. HESS, Irreversible thermodynamics of nonequilibrium alignment phenomena in molecular liquids and in liquid crystals, Z. Naturforsch., 30a, 728-733, 1975.
  • 10. G. A. MAUGrN and R. DROUOT, Thermodynamic modelling of polymers in sol'Utim , [in:] AXELRAD and W . MUSCHIK [Eds.]' Constitutive Laws and Microstructure, Springer Verlag, 1988.
  • 11. E. A . BRENER, H. MOLLER-KRUMBHAAR and R. SPATSCHEK, Coarsening of cracks in a 'Uniaxially strained solid, Phys. Rev. Let. , 86, 7, 1291 --1294, 2001.
  • 12. Z. P . BAZANT and D. NovAK, Probabilistic nonlocal theory for q'Uasibrittle fractLre initiation and size effect. i: theory, J. Eng. Mech., 126, 2, 166- 174, 2000.
  • 13. S. GLUZMAN and D . SORNETTE, Self-consistent theory of rupture by progressive diffuse damage, Physical Review E, 63,6, 066129, 11, 2001.
  • 14. J. V . ANDERSEN, D . SORNETTE and K. LEUNG, Tricritical behaviour in rupture induced by disorder, Physical Review Letters, 78, 11 , 2140- 2143, 1997.
  • 15. R. L. BLUMBERG SELINGER, YHANG-GANG WANG, W. GELBART and A. BEN-3HAUL, Statistical-themodynamic approach to fracture, Physical Review A, 43, 8, 4396- 440. , 1991.
  • 16. S. ZAPPERI, P. RAY , H. E. STANLEY and A. VESPIGNANI, First-order transiti01. in the breakdown of disordered media, Physical Review Letters, 7, 8, 1408- 1411, 1997.
  • 17. S. ZAPPERI , P. RAY, H . E. STANLEY and A. VESPIGNANI, Avalanches in breakdown and fracture processes, Physical Review E, 59, 5, 5049- 5057, 1999.
  • 18. P . VAN, C. PAPENFUSS and W. MUSCHIK, Me.soscopic dynamics of microcracks, Fhysical Review E, 62, 5, 6206- 6215 , 2000.
  • 19. S. BLENK, H. EHRENTRAUT, and W. MUSCHIK, Statistical foundation of macnoscopic balances for liquid crystals in alignment tensor formulation, Physica A, 174, 1:9- 138, 1991.
  • 20. S . BLENK, H . EHRENTRAUT, and W. MUSCHIK, Orientation balances for liquid crystals and their repres entation by alignment tensors, Mol. Cryst. Liqu. Cryst., 204, 1 ~3 - 141, 1991.
  • 21. C. PAPENFUSS, Theory of liquid crystals as an example of m esoscopic continuum Mechanics, Computational Materials Science, 19, 45- 52, 2000.
  • 22. H . EHRENTRAUT, A unified mesoscopic continuum theory of uniaxial and biaxia liquid crystals, Wissenschaft und Technik Verlag, Berlin 1996.
  • 23. H. EHRENTRAUT, W. MUSCHIK, and C. PAPENFUSS, Mesoscopically derived oriettation dynamics of liquid crystals, J. Non-Equilib. Thermodyn. , 22, 285--298, 1997.
  • 24. W . MUSCHIK, An amendment to the second law of thermodynamics, J. Non-Equilib. Thermodyn., 21, 175- 192, 1996.
  • 25. S. BLENK, H. EHRENTRAUT, and W. MUSCHlK, Macroscopic constitutive equatilTl.s for liquid crystals induced by their mesoscopic orientation distribution, Int .. J. Engn;. Sci ., 30, 9, 1127- 1143, 1992.
  • 26. S. BLENK and W. MUSCHIK, Mesoscopic concepts for' constitutive equations of rematic liquid cry.stals in alignment tensor formulation , ZAMM, 73, 4- 5, T331- T333, 199:.
  • 27. P. VAN, C. PAPENFUSS, and W. MUSCHIK, Griffith cracks in the mesoscopic micro crack theory, published online, Condensed Matter, abstract, cond-matj0211207; sent t Phys. Rev. E, 2002.
  • 28. H. EHRENTRAUT and W . MUSCHIK, On symmetric irreducible tensors in d-dimensions, ARI, 51, 1998.
  • 29. N. F. MOTT, Brittle fracture in mild steel plates, Engineering, 165, 1948.
  • 30. B. LAWN . Fracture of brittle solids, Cambridge University Press, Cambridge 1993.
  • 31. A. A. GRIFFITH , The theory of rupture, Trans. First IntI. Congo Appl. Mech., Delft 1924.
  • 32. P. VAN. Internal thermodynamic va1'iables and failure of microcracked materials, J. Non Equilib. Thermodyn., 26, 2, 167-- 189, 200l.
  • 33. O. PENROSE and P . C. FIFE, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Physica D, 43, 44- 62, 1990.
  • 34. L. O . EASTGATE, J. P. SETHNA, M. RAUSCHER, T . CRETEGNY, C. S. CHEN, and C. R. MYERS, Fracture in mode i using a conserved phase-field model, Phys. Rev. E, 65, 3, 2002 .
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0002-0110
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