Eulerian conjugate stress and strain

Andrew Norris
2008 Journal of Mechanics of Materials and Structures  
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
more » ... 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.
doi:10.2140/jomms.2008.3.243 fatcat:zphsxft53rh57mt3colm5c5tt4