A theory for small deformation analysis of growing bodies with an application to the winding of magnetic tape packs


A general theory is proposed for the analysis of small deformations in growing bodies. The growing nature of these bodies is due to reasons that are not related to the main deformation process, as for example is the case in solidifying or melting bodies and in magnetic tapes during winding. We assume that the growing boundary is completely described in time. The strain tensor in such growing bodies does not satisfy the compatibility conditions. However, the strain rate tensor satisfies the compatibility condition and as such a hypoelastic constitutive model is proposed as an appropriate elastic model and the whole deformation problem is casted in the form of an initial/boundary value problem. The obtained solution satisfies continuity of deformation and it can easily be extended to account for rate dependent phenomena.

As an application of this theory, a two-dimensional axially symmetric model and its finite element implementation for computing the induced stresses and deformation in a magnetic tape pack during a winding operation, are presented. The effects on the stresses of a tape pack due to a non-uniform across the tape width applied winding tension, are examined and presented.

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Zabaras, N., Liu, S. A theory for small deformation analysis of growing bodies with an application to the winding of magnetic tape packs. Acta Mechanica 111, 95–110 (1995). https://doi.org/10.1007/BF01187730

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  • Constitutive Model
  • Compatibility Condition
  • Induce Stress
  • Small Deformation
  • Elastic Model