On displacement-velocity coupling and the origin of in-plane stress in orthotropic moving continua
Julkaistu sarjassa
Reports of the Department of Mathematical Information Technology. Series B, Scientific computingPäivämäärä
2014In this paper, we address the problem of the origin of in-plane stresses in
continuous, two-dimensional high-speed webs. In the case of thin, slender
webs, a typical modeling approach is the application of a stationary in-plane
model, without considering the effects of in-plane velocity field. However, for
high-speed webs this approach is insufficient, because it neglects the coupling
between the total material velocity and the deformation experienced by the material. By using a mixed Lagrange–Euler approach in model derivation, the
solid continuum problem can be transformed to solid a continuum flow problem. Mass conservation in the flow problem, and the behaviour of free edges
in the two-dimensional case, are both seen to influence the velocity field. We
concentrate on the steady-state solutions of the model, and study briefly the
coupled nature of material viscoelasticity and transport velocity in one dimension. Analytical solutions of the one-dimensional equation are presented with
both elastic and viscoelastic material assumptions. Numerical solution of the
two-dimensional elastic problem is also presented. Due to the nature of the
velocity-dependent contraction, a nonlinear FEM solution procedure is used.
The results indicate that inertial effects produce an additional contribution to
elastic contraction in unsupported, free webs.
...
Julkaisija
University of JyväskyläISBN
978-951-39-6937-0ISSN Hae Julkaisufoorumista
1456-436XAsiasanat
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