Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on non-homogeneous deformations with homogeneous Cauchy stress
  for a strictly rank-one convex energy in isotropic hyperelasticity   It has recently been shown that for a Cauchy stress response induced by a
strictly rank-one convex hyperelastic energy potential, a homogeneous Cauchy
stress tensor field cannot correspond to a non-homogeneous deformation if the
deformation gradient has discrete values, i.e. if the deformation is piecewise
affine linear and satisfies the Hadamard jump condition. In this note, we
expand upon these results and show that they do not hold for arbitrary
deformations by explicitly giving an example of a strictly rank-one convex
energy and a non-homogeneous deformation such that the induced Cauchy stress
tensor is constant. In the planar case, our example is related to another
previous result concerning criteria for generalized convexity properties of
conformally invariant energy functions, which we extend to the case of strict
rank-one convexity.

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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph