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Geometrical aspects of surface morphogenesis.

T N Hart1, L E Trainor

  • 1Department of Physics, University of Toronto, Ontario, Canada.

Journal of Theoretical Biology
|June 8, 1989
PubMed
Summary

This study presents a general theory for the morphogenesis of thin deformable sheets under local stress. It provides equations for large deformations, linking surface geometry to local tension.

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Area of Science:

  • Physics
  • Materials Science
  • Mechanics of Materials

Background:

  • Morphogenesis of thin deformable sheets is crucial in various scientific fields.
  • Understanding large deformations and local stress effects is essential for accurate modeling.

Purpose of the Study:

  • To develop a general formalism for the deformation of thin sheets under isotropic local body stress.
  • To derive equations based on shell theory, accounting for large deformations.
  • To establish a relationship between surface metric tensor and local tension.

Main Methods:

  • Development of a general theoretical framework for sheet deformation.
  • Application of shell theory with geometric corrections for large deformations.
  • Solving derived equations to relate surface metric tensor to local tension.
  • Numerical example using a simple threshold model.

Main Results:

  • A set of equations governing the deformation of thin sheets under local stress.
  • The surface metric tensor is determined as a function of local tension under specific conditions.
  • Demonstration of the formalism with a numerical example.

Conclusions:

  • The presented formalism provides a robust method for analyzing the morphogenesis of thin deformable sheets.
  • The findings offer insights into the relationship between stress, deformation, and geometry in thin structures.
  • The study validates the theoretical framework with a numerical example, applicable to various scientific and engineering problems.

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