Eulerian conjugate stress and strain

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Abstract

New results are presented for the stress conjugate to arbitrary Eulerian strain measures. The conjugate stress depends on two arbitrary quantities: the strain measure f(V) and the corotational rate defined by the spin Ω. It is shown thaf for every choice of f there is a unique spin, called the f-spin, which makes the conjugate stress as close as possible to the Cauchy stress. The f-spin reduces to the logarithmic spin when the strain measure is the Hencky strain In V. The formulation and !he results emphasize the similarities in form of the Eulerian and Lagrangian stresses conjugate to the strains f(V) and f(U), respectively. Many of the results involve the solution to the equation AX - XA = Y, which is presented in a succinct format.

Original languageEnglish (US)
Pages (from-to)243-260
Number of pages18
JournalJournal of Mechanics of Materials and Structures
Volume3
Issue number2
DOIs
StatePublished - Feb 2008

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Applied Mathematics

Keywords

  • Conjugate
  • Corotational
  • Eulerian
  • Hencky
  • Logarithmic strain rate
  • Stress

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