Vol. 3, No. 2, 2008

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Eulerian conjugate stress and strain

Andrew N. Norris

Vol. 3 (2008), No. 2, 243–260

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 lnV. 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.

conjugate, Eulerian, stress, logarithmic strain rate, Hencky, corotational
Received: 20 August 2007
Revised: 18 September 2007
Accepted: 16 September 2007
Published: 1 February 2008
Andrew N. Norris
Mechanical and Aerospace Engineering
Rutgers University
98 Brett Road
Piscataway NJ 08854-8058
United States