Abstract
In this paper, the theoretical elements of the stream-tube method are considered for the evaluation of strain-rate and strain histories required for the descriptions of memory-integral equations. One interest of the stream-tube analysis lies in the fact that the computation is performed in a transformed domain of the physical domain where the mapped streamlines are parallel and straight. Unknown mapping functions are used for analytic expressions of tensor components, for two- and three-dimensional flow situations. Calculations in three-dimensional flows for corotational models indicate that the relevant analytic expressions deduced from corotating frame determination are too complicated to be realistic for computation, but are exploitable for two-dimensional flow simulations. Strain histories are presented for two- and three-dimensional flows and may be applied to evaluation of stresses in both cases, when using codeformational constitutive equations.
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Clermont, JR. Calculation of kinematic histories in two- and three-dimensional flows using streamline coordinate functions. Rheologica Acta 32, 82–93 (1993). https://doi.org/10.1007/BF00396680
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DOI: https://doi.org/10.1007/BF00396680