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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 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
ln 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
A X
− X A
= Y ,
which is presented in a succinct format.
Keywords
conjugate, Eulerian, stress, logarithmic strain rate,
Hencky, corotational
Milestones
Received: 20 August 2007
Revised: 18 September 2007
Accepted: 16 September 2007
Published: 1 February 2008