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From a distance: Shuttleworth revisited.

Stefanie Heyden1, Nicolas Bain2

  • 1ETH Zürich, Institute for Building Materials, 8093 Zürich, Switzerland. stefanie.heyden@mat.ethz.ch.

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Summary
This summary is machine-generated.

The Shuttleworth equation, used for soft surfaces, is re-evaluated for large deformations. Elastic constants depend on the stress measure used, impacting surface elastic moduli estimations.

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Area of Science:

  • Materials Science
  • Solid Mechanics
  • Surface Physics

Background:

  • The Shuttleworth equation is a linear stress-strain relationship commonly applied to model soft surface behavior.
  • Its applicability to materials undergoing large deformations is currently under investigation and debate.

Purpose of the Study:

  • To derive the constitutive behavior of surfaces within a finite kinematics framework to accommodate large deformations.
  • To analyze the influence of different stress measures on elastic constants and surface elastic moduli.
  • To investigate the effect of surface relaxation on the estimation of surface elastic moduli.

Main Methods:

  • Derivation of constitutive behavior using the general framework of finite kinematics.
  • Distinguishing between finite and infinitesimal surface relaxation prior to infinitesimal applied deformation.
  • Analysis of elastic constants in both finite and linearized settings.

Main Results:

  • The Shuttleworth equation corresponds to the Cauchy stress measure in a fully linearized context.
  • Measured elastic constants are shown to be dependent on the chosen stress measure, irrespective of whether finite or linearized cases are considered.
  • Surface relaxation significantly impacts the estimation of surface elastic moduli.

Conclusions:

  • The validity of the Shuttleworth equation under large deformations requires careful consideration of the stress measure.
  • Results provide physical insights into the behavior of soft surfaces and the influence of pre-applied deformation.
  • Accurate estimation of surface elastic moduli necessitates accounting for surface relaxation effects and the choice of stress measure.