Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Field Modeling of Fracture and Stress Induced Phase Transitions   We present a continuum theory to describe elastically induced phase
transitions between coherent solid phases. In the limit of vanishing elastic
constants in one of the phases, the model can be used to describe fracture on
the basis of the late stage of the Asaro-Tiller-Grinfeld instability. Starting
from a sharp interface formulation we derive the elastic equations and the
dissipative interface kinetics. We develop a phase field model to simulate
these processes numerically; in the sharp interface limit, it reproduces the
desired equations of motion and boundary conditions. We perform large scale
simulations of fracture processes to eliminate finite-size effects and compare
the results to a recently developed sharp interface method. Details of the
numerical simulations are explained, and the generalization to multiphase
simulations is presented.

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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas