  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 be rather insensitive
to defects and to have a very high fracture toughness. Their deterministic
behavior has been intensely studied, but statistical studies have been rare and
is so far there is no undisputed theoretical basis for the probability
distribution of strength of nacre. This paper presents a numerical and
theoretical study of the PDF of strength and of the corresponding statistical
size effect. After a reasonable simplifications of the shear bonds, an axially
loaded lamellar shell is statistically modelled as a square fishnet pulled
diagonally. A finite element (FE) model is developed and used in Monte Carlo
simulations of strength. An analytical model for failure probability of the
fishnet is developed and matched to the computed statistical histograms of
strength for various sizes. It appears that, with increasing size, the pdf of
strength slowly transits from Gaussian to Weilbull distribution but the
transition is different from that previously obtained at Northwestern for
quasibrittle materials of random heterogeneous mesostructure.
