Fishnet statistics for probabilistic strength and scaling of nacreous imbricated lamellar materials

@article{Luo2017FishnetSF,
  title={Fishnet statistics for probabilistic strength and scaling of nacreous imbricated lamellar materials},
  author={Wen-fei Luo and Zdeněk P. Ba{\vz}ant},
  journal={Journal of The Mechanics and Physics of Solids},
  year={2017},
  volume={109},
  pages={264-287}
}
  • Wen-fei Luo, Z. Bažant
  • Published 6 June 2017
  • Materials Science
  • Journal of The Mechanics and Physics of Solids
Fishnet model with order statistics for tail probability of failure of nacreous biomimetic materials with softening interlaminar links
Fishnet model with order statistics for tail probability of failure of nacreous biomimetic materials with softening interlaminar links
The staggered (or imbricated) lamellar “brick-and-mortar” nanostructure of nacre endows nacre with strength and fracture toughness values exceeding by an order of magnitude those of the constituents,
Fishnet model for failure probability tail of nacre-like imbricated lamellar materials
TLDR
A statistical model of strength that resembles a fishnet pulled diagonally, captures the tail of pdf of strength and, importantly, allows analytical safety assessments of nacreous materials is outlined.
General Fishnet Statistics of Strength: Nacreous, Biomimetic, Concrete, Octet-Truss, and Other Architected or Quasibrittle Materials
The fishnet probabilistic model was recently developed to characterize the strength distribution of nacre-like biomimetic materials. It reveals that the unique fishnet-like connectivity of the
General Fishnet Statistics of Strength: Nacreous, Biomimetic, Concrete, Octet-Truss, and Other Architected or Quasibrittle Materials
The fishnet probabilistic model was recently developed to characterize the strength distribution of nacre-like biomimetic materials. It reveals that the unique fishnet-like connectivity of the
Fishnet Statistical Size Effect on Strength of Materials With Nacreous Microstructure
The statistical size effect has generally been explained by the weakest-link model, which is valid if the failure of one representative volume element (RVE) of material, corresponding to one link,
FISHNET STATISTICS FOR QUASIBRITTLE MATERIALS WITH NACRE-LIKE ALTERNATING SERIES AND PARALLEL LINKS : DESIGN FOR FAILURE PROBABILITY < 10 − 6
The failure probability of engineering structures such as bridges, airframes and MEMS ought to be 10−6. This is a challenge. For perfectly brittle and ductile materials obeying the Weibull or
Fishnet model for failure probability of nacre-like imbricated lamellar materials and Monte Carlo verification
The conference paper reviews recent studies at Northwestern University, in which the connectivity in nacreous staggered lamellar systems is, for probabilistic analysis, represented as a fishnet
Design of quasibrittle materials and structures to optimize strength and scaling at probability tail: an apercu
  • Z. Bažant
  • Physics
    Proceedings of the Royal Society A
  • 2019
TLDR
This inaugural article reviews recent results towards the quasibrittle materials such as concretes, rocks, tough ceramics, fibre composites, bone and most materials on the micrometer scale, and finds the fishnet to be the third strength probability model that is amenable to an analytical solution of the strength probability distribution.
...
...

References

SHOWING 1-10 OF 42 REFERENCES
Fishnet Statistics for Strength Scaling of Nacreous Imbricated Laminar Materials
Similar to nacre or brick-and-mortar structures, imbricated lamellar structures are widely found in natural and man-made materials and are of interest for biomimetics. These structures are known to
Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics
TLDR
A recently proposed theory for the strength cdf of quasibrittle structure is refined by deriving it from fracture mechanics of nanocracks propagating by small, activation-energy-controlled, random jumps through the atomic lattice, which provides a plausible physical justification of the power law for subcritical creep crack growth.
Scaling theory for quasibrittle structural failure.
  • Z. Bažant
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 2004
This inaugural article has a twofold purpose: (i) to present a simpler and more general justification of the fundamental scaling laws of quasibrittle fracture, bridging the asymptotic behaviors of
Scaling of quasibrittle fracture: asymptotic analysis
Fracture of quasibrittle materials such as concrete, rock, ice, tough ceramics and various fibrous or particulate composites, exhibits complex size effects. An asymptotic theory of scaling governing
Statistics of strength of ceramics: finite weakest-link model and necessity of zero threshold
It is argued that, in probabilistic estimates of quasibrittle structure strength, the strength threshold should be considered to be zero and the distribution to be transitional between Gaussian and
Subcritical crack growth law and its consequences for lifetime statistics and size effect of quasibrittle structures
For brittle failures, the probability distribution of structural strength and lifetime are known to be Weibullian, in which case the knowledge of the mean and standard deviation suffices to determine
...
...