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Curl bounds grad on SO(3)

Ingo Münch, Patrizio Neff (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Let F p GL ( 3 ) be the plastic deformation from the multiplicative decomposition in elasto-plasticity. We show that the geometric dislocation density tensor of Gurtin in the form Curl [ F p ] · ( F p ) T applied to rotations controls the gradient in the sense that pointwise R C 1 ( 3 , SO ( 3 ) ) : Curl [ R ] · R T 𝕄 3 × 3 2 1 2 D R 27 2 . This result complements rigidity results [Friesecke, James and Müller, Comme Pure Appl. Math. 55 (2002) 1461–1506; John, Comme Pure Appl. Math. 14 (1961) 391–413; Reshetnyak, Siberian Math. J. 8 (1967) 631–653)] as well as an associated linearized theorem...

Curl bounds Grad on SO(3)

Patrizio Neff, Ingo Münch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Let F p GL ( 3 ) be the plastic deformation from the multiplicative decomposition in elasto-plasticity. We show that the geometric dislocation density tensor of Gurtin in the form Curl [ F p ] · ( F p ) T applied to rotations controls the gradient in the sense that pointwise R C 1 ( 3 , SO ( 3 ) ) : Curl [ R ] · R T 𝕄 3 × 3 2 1 2 D R 27 2 . This result complements rigidity results [Friesecke, James and Müller, Comme Pure Appl. Math.55 (2002) 1461–1506; John, Comme Pure Appl. Math.14 (1961) 391–413; Reshetnyak, Siberian Math. J.8 (1967) 631–653)] as well as an associated linearized theorem saying...

Curvature and torsion formulas for conflict sets

Martijn van Manen (2003)

Banach Center Publications

Conflict set are the points at equal distance from a number of manifolds. Known results on the differential geometry of these sets are generalized and extended.

Curvature functionals for curves in the equi-affine plane

Steven Verpoort (2011)

Czechoslovak Mathematical Journal

After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail. Notice. An extended version of this article is available on arXiv:0912.4075.

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