Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reduced polynomial invariant integrity basis for in-plane
  magneto-mechanical loading   The description of the behavior of a material subjected to multi-physics
loadings requires the formulation of constitutive laws that usually derive from
Gibbs free energies, using invariant quantities depending on the considered
physics and material symmetries. On the other hand, most of crystalline
materials can be described by their crystalline texture and the associated
preferred directions of strong crystalline symmetry (the so-called fibers).
Moreover, among the materials produced industrially, many are manufactured in
the form of sheets or of thin layers. This article has for object the study of
the magneto-mechanical coupling which is a function of the stress $\sigma$ and
the magnetization M. We consider a material with cubic symmetry whose texture
can be described by one of three fibers denoted as $\theta$, $\gamma$ or
$\alpha$ ' , and which is thin enough so that both the stress and the
magnetization can be considered as in-plane quantities. We propose an algorithm
able to derive linear relations between the 30 cubic invariants I k of a
minimal integrity basis describing a magneto-elastic problem, when they are
restricted to in-plane loading conditions and for different fiber orientations.
The algorithm/program output is a reduced list of invariants of cardinal 7 for
the {100}-oriented $\theta$ fiber, of cardinal 15 for the {110}-oriented
$\alpha$ ' fiber and of cardinal 8 for the {111}-oriented $\gamma$ fiber. This
reduction (compared to initial cardinal 30) can be of great help for the
formulation of low-parameter macroscopic magneto-mechanical models.

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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg