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Inverted cones and their elastic creases.

Keith A Seffen1

  • 1Advanced Structures Group Laboratory, Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom.

Physical Review. E
|January 14, 2017
PubMed
Summary

This study precisely models the elastic inversion of a cone, accurately predicting crease shape and stored strain energy using a cylindrical shell analogy. The findings validate assumptions against finite element analysis for various cone geometries.

Area of Science:

  • Solid Mechanics
  • Materials Science
  • Geometric Mechanics

Background:

  • Creases in conical structures are common in natural and engineered systems.
  • Understanding crease formation is crucial for predicting material behavior under stress.
  • Previous studies often lack precise analytical models for controlled crease formation.

Purpose of the Study:

  • To develop an analytical model for the elastic inversion of a right circular cone.
  • To precisely define the characteristic width and shape of the boundary layer deformation (crease).
  • To calculate the strain energy and applied force during cone inversion.

Main Methods:

  • Utilizing a cylindrical shell analogy to simplify the deformation analysis.
  • Solving the governing equation of deformation with carefully defined assumptions and boundary conditions.

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  • Deriving closed-form expressions for crease shape and inversion force.
  • Comparing analytical predictions with geometrically nonlinear, large displacement finite element analysis (FEA).

    • Main Results:

    • An exact expression for the crease shape was derived.
    • The characteristic crease width was accurately predicted for both shallow and steep cones.
    • Strain energy and applied inversion force were computed using an energy method.
    • Analytical results showed excellent agreement with FEA data.

    Conclusions:

    • The cylindrical shell analogy and derived analytical model provide accurate predictions for cone inversion.
    • The methodology offers a reliable approach for studying controlled crease formation in conical shells.
    • This work complements existing research on creases formed during less controlled processes like sheet crumpling.