Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Failure Probabilities and Tough-Brittle Crossover of Heterogeneous
  Materials with Continuous Disorder   The failure probabilities or the strength distributions of heterogeneous 1D
systems with continuous local strength distribution and local load sharing have
been studied using a simple, exact, recursive method. The fracture behavior
depends on the local bond-strength distribution, the system size, and the
applied stress, and crossovers occur as system size or stress changes. In the
brittle region, systems with continuous disorders have a failure probability of
the modified-Gumbel form, similar to that for systems with percolation
disorder. The modified-Gumbel form is of special significance in weak-stress
situations. This new recursive method has also been generalized to calculate
exactly the failure probabilities under various boundary conditions, thereby
illustrating the important effect of surfaces in the fracture process.

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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
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The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics