Abstract
The paper presents the state-of-the-art algorithmic developments for
simulating the fracture of disordered quasi-brittle materials using
discrete lattice systems. Large scale simulations are often required
to obtain accurate scaling laws; however, due to computational
complexity, the simulations using the traditional algorithms were limited to
small system sizes. We have developed two algorithms: a
multiple sparse Cholesky downdating scheme for simulating 2D random
fuse model systems, and a block-circulant preconditioner for simulating
3D random fuse model systems. Using these algorithms, we were able to
simulate fracture of {\it largest ever} lattice system sizes ($L = 1024$ in 2D,
and $L = 64$ in 3D) with extensive statistical sampling. Our recent
simulations on $1024$ processors of Cray-XT3 and IBM Blue-Gene/L have further
enabled us to explore fracture of 3D lattice systems of size $L = 200$,
which is a significant computational achievement.
These largest ever numerical simulations have enhanced our
understanding of physics of fracture; in particular, we analyze
damage localization and its deviation from percolation behavior,
scaling laws for damage density, universality of fracture strength
distribution, size effect on the mean fracture strength, and finally the scaling of
crack surface roughness.
