Displaying similar documents to “Invariant line integrals in the theory of defective crystals”

General and physically privileged solutions to certain symmetric systems of linear P.D.E.s with tensor functionals as unknowns

Adriano Montanaro, Diego Pigozzi (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We characterize the general solutions to certain symmetric systems of linear partial differential equations with tensor functionals as unknowns. Then we determine the solutions that are physically meaningful in suitable senses related with the constitutive functionals of two simple thermodynamic bodies with fading memory that are globally equivalent, i.e. roughly speaking that behave in the same way along processes not involving cuts. The domains of the constitutive functionals are nowhere...

Curl bounds grad on SO(3)

Ingo Münch, Patrizio Neff (2008)

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 ( ℝ 3 , SO ( 3 ) ) : ∥ Curl [ R ] · R T ∥ 𝕄 3 × 3 2 ≥ 1 2 ∥ D R ∥ 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...