Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double-phase-field formulation for mixed-mode fracture in rocks   Cracking of rocks and rock-like materials exhibits a rich variety of patterns
where tensile (mode I) and shear (mode II) fractures are often interwoven.
These mixed-mode fractures are usually cohesive (quasi-brittle) and frictional.
Although phase-field modeling is increasingly used for rock fracture
simulation, no phase-field formulation is available for cohesive and frictional
mixed-mode fracture. To address this shortfall, here we develop a
double-phase-field formulation that employs two different phase fields to
describe cohesive tensile fracture and frictional shear fracture individually.
The formulation rigorously combines the two phase fields through three
approaches: (i) crack-direction-based decomposition of the strain energy into
the tensile, shear, and pure compression parts, (ii) contact-dependent
calculation of the potential energy, and (iii) energy-based determination of
the dominant fracturing mode in each contact condition. We validate the
proposed model, both qualitatively and quantitatively, with experimental data
on mixed-mode fracture in rocks. The validation results demonstrate that the
double-phase-field model -- a combination of two quasi-brittle phase-field
models -- allows one to directly use material strengths measured from
experiments, unlike brittle phase-field models for mixed-mode fracture in
rocks. Another standout feature of the double-phase-field model is that it can
simulate, and naturally distinguish between, tensile and shear fractures
without complex algorithms.

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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: math