Eulerian conjugate stress and strain

Details Eulerian conjugate stress and strain Eulerian conjugate stress and strain

2007-08-20

arxiv.org/abs/0708.2736v2

J. Mech. Materials Struct. 3(2), 243-260, 2008

Physics

Condensed Matter

Materials Science

17 pages

Scientific paper

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 \Omega. It is shown that 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 log(V). The formulation and the 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.

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