FIRST-PASSAGE PERCOLATION, SEMI-DIRECTED BERNOULLI PERCOLATION AND FAILURE IN BRITTLE MATERIALS

We present a two-dimensional, quasistatic model of Fracture in disorde red brittle materials that contains elements of first-passage percolat ion, i.e., we use a minimum-energy-consumption criterion For the fract ure path. The first-passage model is employed in conjunction with a '' semi-directed'' Bernoulli percolation model, for which we calculate cr itical properties such as the correlation length exponent v(sdir) and the percolation threshold p(c)(sdir). Among other results, our numeric s suggest that v(sdir) is exactly 3/2, which lies between the correspo nding known values in the literature for usual and directed Bernoulli percolation. We also iind that the well-known scaling relation between the ''wandering'' and energy fluctuation exponents breaks down in the vicinity of the threshold for semi-directed percolation. For a restri cted class of materials, we study the dependence of the fracture energ y (toughness) on the width of the distribution of the specific Fractur e energy and find that it is quadratic in the width for small widths f or two different random fields, suggesting that this dependence may be universal.