Second-Order Structured Deformations: Approximation Theorems and Energetics

  • Roberto Paroni
Part of the International Centre for Mechanical Sciences book series (CISM, volume 447)


Recent research on geometrical changes that can occur at different length scales has led to the concept of a structured deformation (k, g, G), see [Del Piero and Owen (1993)]. Structured deformations have been applied to describe geometrical changes associated with slips and the presence of defects in single crystals, with deformations of liquid crystals, with fracture, and with the mixing of different substances [Del Piero and Owen (1993)]. One limitation of structured deformations is that the effects on macroscopic deformation of jumps in the gradients ∇ f m of approximating simple deformations are not captured. Another limitation is the following: Structured deformations lead to the additive decomposition ∇g(x) = G(x) + M(x), where M is a deformation due to disarrangements associated with non-smooth changes at a smaller length scale, but do not reveal any decomposition for ∇2 g(x) which puts into light the effects of deformations at smaller length scales. Finally, definitive refinements of kinematical quantities such as acceleration and stretching are not available through such structured deformations.


Structure Deformation Approximation Theorem Extension Theorem Geometrical Change Small Length Scale 


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© Springer-Verlag Wien 2004

Authors and Affiliations

  • Roberto Paroni
    • 1
  1. 1.Dipartimento di Architettura e PianificazioneUniversità degli Studi di SassariAlgheroItaly

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