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 2D random fuse model systems. Using these algorithms, we were able to simulate fracture of 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.
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