Abstract
The breaking of solids caused by an external load is evidently a problem of technological importance and has been intensively studied for the last hundred years [5.1]. On very small length scales (≤ 10-6 m) fracture is a topic of materials science. From the electronic level [5.2] to the level of dislocations or grain boundaries [5.3] the mechanisms of fracture are highly material dependent. On very large length scales (≥ 10-1 m) the prevention of fracture is studied by engineers. There results are mainly based on experience and depend essentially on the application and the shape of the sample. On intermediate length scales the behavior of the solid can be described by the methods of applied mechanics, i.e., by continuous equations of motion. There exist on this level just a few types of different behaviors — for example elastic, plastic, viscoelastic — each given by its own set of differential equations containing some material-dependent parameters. The relatively general validity of the formalism makes the study of fracture in this intermediate (or mesoscopic) range of length scales particularly attractive to statistical physicists. If the reader wants to know more about recent developments in this direction I recommend [5.4].
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References
H. Liebowitz, ed.: Fracture, Vols. I–VII, (Academic, New York 1986)
C.L. Briant, R.P. Messmer: Phil. Mag. B 42, 569 (1980);
M.E. Eberhart, D.D. Vvdensky: Phys. Rev. Lett. 58, 61 (1987)
E.C. Aifantis: J. Eng. Mater. Technol. 106, 326 (1986)
H.J. Herrmann, S. Roux, eds.: Statistical Models for the Fracture of Disordered Media (Elsevier, Amsterdam 1990)
D. Broek: Elementary Engineering Fracture Mechanics (Martinus NijhofF, Dordrecht 1986)
W. Nowacki: Theory of Micropolar Elasticity, CISM Int. Center for Mechanical Sci., Courses and Lectures, No. 25 (Springer, Heidelberg 1970)
D.A. Kessler, J. Koplik, H. Levine: Adv. Phys. 37, 255 (1988)
H. Van Damme, E. Alsac, C. Laroche: C.R. Acad. Sci., Ser.II 309, 11 (1988):
H. Van Damme, in: The Fractal Approach to Heterogeneous Chemistry, ed. by D. Avnir (Wiley, New York 1989), p. 199
L.D. Landau, E.M. Lifshitz: Elasticity (Pergamon, Oxford 1960), p. 130
M. Barber, J. Donley, J.S. Langer: Phys. Rev. A 40, 366 (1989)
S.S. Rao: The Finite Element Method in Engineering (Pergamon, Oxford 1982);
P. Tong, J.N. Rossettos: Finite Element Method: Basic Technique and Implementation (MIT Press, Cambridge 1977)
G.G. Batrouni, A. Hansen: J. Stat. Phys. 52, 747 (1988)
L. de Arcangelis, S. Redner, H.J. Herrmann: J. de Phys. Lett. 46, L585 (1985)
L. Niemeyer, L. Pietronero, H.J. Wiesmann: Phys. Rev. Lett. 52, 1033 (1984)
H. Takayasu, in: Fractals in Physics, ed. by L. Pietronero, E. Tossatti (Elsevier, Amsterdam 1986), p. 181;
H. Takayasu: Phys. Rev. Lett. 54, 1099 (1985)
S. Feng, P.N. Sen: Phys. Rev. Lett. 52, 216 (1984)
Y. Kantor, I. Webman: Phys. Rev. Lett. 52, 1891 (1984)
S. Roux, E. Guyon: J. de Phys. Lett. 46, L999 (1985)
R.J. Roark, W.C. Young: Formulas for Stress and Strain (McGraw-Hill, Tokyo 1975), p. 89
H. Yan, G. Li, L.M. Sander: Europhys. Lett. 10, 7 (1989)
E. Louis, F. Guinea, F. Flores, in: Fractals in Physics, ed. by L. Pietronero, E. Tossatti (Elsevier, Amsterdam 1986);
E. Louis, F. Guinea: Europhys. Lett. 3, 871 (1987)
P. Meakin: Thin Solid Films 151, 165 (1987)
P. Meakin, G. Li, L.M. Sander, E. Louis, F. Guinea: J. Phys. A 22, 1393 (1989)
B. Kahng, G.G. Batrouni, S. Redner, L. de Arcangelis, H.J. Herrmann: Phys. Rev. B 37, 7625 (1988)
P.M. Duxbury, P.D. Beale, P.L. Leath: Phys. Rev. Lett. 57, 1052 (1986);
P.M. Duxbury, P.L. Leath, P.D. Beale: Phys. Rev. B 36, 367 (1987)
P.D. Beale, D.J. Srolovitz: Phys. Rev. B 37, 5500 (1988)
L. de Arcangelis, H.J. Herrmann: Phys. Rev. B 39, 2678 (1989)
Y. Termonia, P. Meakin, P. Smith: Macromolecules 18, 2246 (1985)
P. Meakin, in: Ref. [5.4]
E.L. Hinrichsen, A. Hansen, S. Roux: Europhys. Lett. 8,1 (1989)
H.J. Herrmann, A. Hansen, S. Roux: Phys. Rev. B 39, 637 (1989)
H.J. Herrmann, J. Kertész, L. de Arcangelis: Europhys. Lett. 10, 147 (1989)
T.A. Witten, L.M. Sander: Phys. Rev. Lett. 47, 1400 (1981)
Y.S. Li, P.M. Duxbury: Phys. Rev. B 38, 9257 (1988)
F. Family, Y.C. Zhang, T. Vicsek: J. Phys. A 19, L733 (1986)
P.D. Beale, P.M. Duxbury: Phys. Rev. B 37, 2785 (1988)
L. de Arcangelis, A. Hansen, H.J. Herrmann, S. Roux: Phys. Rev. B 40, 877 (1989)
A. Hansen, S. Roux, H.J. Herrmann: J. Phys. France 50, 733 (1989)
C. Tang: Phys. Rev. A 31, 1977 (1985);
J. Szép, J. Cserti, J. Kertész: J. Phys. A 18, L413 (1985);
J. Nittmann, H.E. Stanley: Nature 321, 661 (1986);
J. Kertész, T. Vicsek: J. Phys. A 19, L257 (1986)
J. Fernandez, F. Guinea, E. Louis: J. Phys. A 21, L301 (1988)
B.B. Mandelbrot, T. Vicsek: J. Phys. A 22, L377 (1989)
F. Family, D.E. Platt, T. Vicsek: J. Phys. A 20, L1177 (1987)
J.P. Eckmann, P. Meakin, I. Procaccia, R. Zeitak: Phys. Rev. A 39, 3185 (1989)
M.J. Blackburn, W.H. Smyrl, J.A. Feeney, in: Stress Corrosion in High Strength Steels and in Titanium and Aluminium Alloys, ed. by B.F. Brown (Naval Research Lab., Washington 1972), p. 344
S. Roux: J. Stat. Phys. 48, 201 (1987)
E.J. Gumbel: Statistics of Extremes (Columbia University, New York 1958)
J. Galambos: The Asymptotic Theory of Extreme Order Statistics (Wiley, New York 1978)
P.M. Duxbury, Y.S. Li, in: Proc. of the SIAM Conf. on Random Media and Composites, ed. by R.V. Cohn and G.W. Milton (SIAM, Philadelphia 1989)
G. Paladin, A. Vulpiani: Phys. Rep. 156, 147 (1987);
L. de Arcangelis, S. Redner, A. Coniglio: Phys. Rev. B 31, 4725 (1985)
T.C. Halsey, P. Meakin, I. Procaccia: Phys. Rev. Lett. 56, 854 (1986)
B.B. Mandelbrot, D.E Passoja, A.J. Paulley: Nature 308, 721 (1984);
C.S. Pande, L.E. Richards, N. Louat, B.D. Dempsey, A.J. Schwoble: Acta Metall. 35, 1633 (1987)
S.R. Brown, C.H. Scholz: J. Geophys. Res. 90, 12575 (1985)
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Herrmann, H.J. (1991). Fractures. In: Bunde, A., Havlin, S. (eds) Fractals and Disordered Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51435-7_5
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