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 . 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

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... ults 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.