Displaying similar documents to “Undecidability of Topological and Arithmetical Properties of Infinitary Rational Relations”

Curl bounds Grad on SO(3)

Patrizio Neff, Ingo Münch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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, (2002) 1461–1506; John, (1961) 391–413; Reshetnyak, (1967) 631–653)] as well as an associated linearized theorem saying...

Characterization of the limit load in the case of an unbounded elastic convex

Adnene Elyacoubi, Taieb Hadhri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this work we consider a solid body Ω 3 constituted by a nonhomogeneous elastoplastic material, submitted to a density of body forces λ f and a density of forces λ g acting on the boundary where the real λ is the loading parameter. The problem is to determine, in the case of an unbounded convex of elasticity, the Limit load denoted by λ ¯ beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri,   (1995) 391–419]. Then assuming...