Fracturing of brittle homogeneous solids: Finite-size scalings.

@article{Tzschichholz1995FracturingOB,
  title={Fracturing of brittle homogeneous solids: Finite-size scalings.},
  author={Tzschichholz},
  journal={Physical review. B, Condensed matter},
  year={1995},
  volume={52 13},
  pages={
          9270-9274
        }
}
  • Tzschichholz
  • Published 3 June 1995
  • Materials Science, Physics, Medicine
  • Physical review. B, Condensed matter
Using a two-dimensional lattice model we investigate the crack growth under the influence of remote tensile forces as well as due to an internally applied pressure (hydraulic fracturing). For homogeneous elastic properties we present numerical finite-size scalings for the breaking stresses and pressures in terms of crack lengths and lattice sizes. Continuum theory predicts for the tensile and for the pressure problem identical scaling functions. Our findings for the tensile problem are in very… 
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References

SHOWING 1-10 OF 19 REFERENCES
Peeling instability in Cosserat-like media.
  • Tzschichholz
  • Materials Science, Medicine
    Physical review. B, Condensed matter
  • 1992
TLDR
A finite-size scaling analysis of the rupture of a two-dimensional square lattice where bonds are elastic beams breaking only through longitudinal stretching at randomly chosen uniform distributed breaking strengths finds the relationship between critical stresses and crack lengths is accurately described by a well-known exact expression from symmetric continuum elasticity.
Beam model for hydraulic fracturing.
TLDR
Numerically the shape of cracks obtained in hydraulic fracturing at constant pressure is investigated using a square lattice beam model with disorder, and the conditions under which the resulting cracks may develop fractal patterns are discussed.
Simulations of pressure fluctuations and acoustic emission in hydraulic fracturing.
  • Tzschichholz, Herrmann
  • Materials Science, Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
TLDR
A two-dimensional lattice model is considered to describe the opening of a crack in hydraulic fracturing and the cumulative probability distribution for breaking events of a given energetical magnitude (acoustic emission) is determined.
A simple two-dimensional model for crack propagation
Simple models for crack growth which are closely related to the diffusion-limited aggregation (DLA) model have been explored using computer simulations. In these models the bond-breaking
Fracture of disordered, elastic lattices in two dimensions.
We study via simulation how a lattice breaks if each bond is an elastic beam having longitudinal and flexural breaking thresholds randomly selected according to various probability distributions. We
Fracture of Brittle Solids by Brian Lawn
  • B. Lawn
  • Materials Science, Geology
  • 1993
This is an advanced text for higher degree materials science students and researchers concerned with the strength of highly brittle covalent–ionic solids, principally ceramics. It is a reconstructed
The Theory of Elastic Media with Microstructure and the Theory of Dislocations
Different phenomenological theories of generalized Cosserat continua have been developed in the well-known works of Aero, Eringen, Green, Grioli, Gunther, Koiter, Kuvshinski, Mindlin, Naghdi, Noll,
THE MATHEMATICAL THEORY OF EQUILIBRIUM CRACKS IN BRITTLE FRACTURE
Publisher Summary In recent years, the interest in the problem of brittle fracture and, in particular, in the theory of cracks has grown appreciably in connection with various technical applications.
The Phenomena of Rupture and Flow in Solids
In the course of an investigation of the effect of surface scratches on the mechanical strength of solids, some general conclusions were reached which appear to have a direct bearing on the problem
Simple force and stress multipoles
E. & F. Cosserat (1909) developed a theory in which the mechanical interaction between portions of a body across a surface in it is considered to consist not only of forces distributed over the
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