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Differential growth and instability in elastic shells.

Alain Goriely1, Martine Ben Amar

  • 1Department of Mathematics, University of Arizona, Tucson, 85721, USA. goriely@math.arizona.edu

Physical Review Letters
|August 11, 2005
PubMed
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Differential growth in elastic shells can cause stress and shape instability. Researchers analyzed growth-induced instabilities in shells under pressure or embedded in elastic media to understand these critical changes.

Area of Science:

  • Solid Mechanics
  • Materials Science
  • Biophysics

Background:

  • Differential growth in elastic materials can lead to internal stresses.
  • These stresses, arising from growth incompatibility or external interactions, can trigger shape instabilities.
  • Understanding growth-induced instabilities is crucial for various applications, including tissue engineering and soft robotics.

Purpose of the Study:

  • To investigate the mechanisms of shape instability in growing elastic shells.
  • To analyze the influence of hydrostatic pressure and surrounding elastic media on growth-induced stress.
  • To determine critical parameters leading to different modes of instability.

Main Methods:

  • Computational modeling of elastic shell growth.
  • Analysis of residual stress due to growth incompatibility.

Related Experiment Videos

  • Calculation of contact stress from interaction with surrounding media.
  • Parametric study varying growth and geometric factors.

    • Main Results:

    • Residual and contact stresses were computed as functions of growth and geometry.
    • Critical values for the onset of instability were identified.
    • Different instability modes were observed depending on the analyzed parameters.
    • The study quantifies the relationship between growth parameters and shell instability.

    Conclusions:

    • Growth-induced stresses in elastic shells can lead to significant shape instabilities.
    • Hydrostatic pressure and the surrounding medium are key factors influencing instability.
    • The findings provide insights into predicting and controlling shape changes in growing elastic structures.