Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy Release Rate, the crack closure integral and admissible singular
  fields in Fracture Mechanics   One of the assumptions of Linear Elastic Fracture Mechanics is that the crack
faces are traction-free or, at most, loaded by bounded tractions. The standard
Irwin's crack closure integral, widely used for the computation of the Energy
Release Rate, also relies upon this assumption. However, there are practical
situations where the load acting on the crack boundaries is singular. This is
the case, for instance, in hydraulic fracturing, where the fluid inside the
crack exerts singular tangential tractions at its front. Another example of
unbounded tractions is the case of a rigid line inclusion (anticrack) embedded
into an elastic body. In such situations, the classical Irwin's crack closure
integral fails to provide the correct value of the Energy Release Rate. In this
paper, we address the effects occurring when square-root singular tractions act
at the boundary of a line defect in an elastic solid and provide a
generalisation of Irwin's crack closure integral. The latter yields the correct
Energy Release Rate and allows broad applications, including, among others,
hydraulic fracturing, soft materials containing stiff inclusions, rigid
inclusions, shear bands and cracks characterized by the Gurtin-Murdoch surface
stress elasticity. We present the results in the most general form, where six
Stress Intensity Factors are present: three of them are classical SIFs
corresponding to the modes I-II-III and computed under the assumption of
homogeneous boundary conditions at the defect surfaces, while the other three
SIFs are associated with singular admissible tractions (those that lead to a
finite ERR value). It is demonstrated that this approach resolves an ambiguity
in using the same SIF's terminology in the cases of open cracks and rigid
inclusions, among other benefits.

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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol