Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonsingular stress and strain fields of dislocations and disclinations
  in first strain gradient elasticity   The aim of this paper is to study the elastic stress and strain fields of
dislocations and disclinations in the framework of Mindlin's gradient
elasticity. We consider simple but rigorous versions of Mindlin's first
gradient elasticity with one material length (gradient coefficient). Using the
stress function method, we find modified stress functions for all six types of
Volterra defects (dislocations and disclinations) situated in an isotropic and
infinitely extended medium. By means of these stress functions, we obtain exact
analytical solutions for the stress and strain fields of dislocations and
disclinations. An advantage of these solutions for the elastic strain and
stress is that they have no singularities at the defect line. They are finite
and have maxima or minima in the defect core region. The stresses and strains
are either zero or have a finite maximum value at the defect line. The maximum
value of stresses may serve as a measure of the critical stress level when
fracture and failure may occur. Thus, both the stress and elastic strain
singularities are removed in such a simple gradient theory. In addition, we
give the relation to the nonlocal stresses in Eringen's nonlocal elasticity for
the nonsingular stresses.

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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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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: solv-int
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The categories of this paper are: stat
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The categories of this paper are: math
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org