Elements of Elastic Stability Theory

Knops, R. J.

doi:10.1007/978-3-7091-2582-3_5

Cited by 3 publications

(2 citation statements)

References 67 publications

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“…We shall show in this paper that if the above-mentioned minimum is negative, then linear (spectral) instability is implied. For a more rigorous discussion of stability criteria for nonlinear elasticity, we refer to the book by Marsden and Hughes (1993) and the more recent article by Knops (2001).…”

Section: Introductionmentioning

confidence: 99%

Stability of pear-shaped configurations bifurcated from a pressurized spherical balloon

Fu¹,

Xie²

2014

Journal of the Mechanics and Physics of Solids

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It is well-known that for most spherical rubber balloons the pressure versus volume curve associated with uniform inflation has an N-shape (the pressure increases rapidly to a maximum, falls to a minimum, and subsequently increases monotonically), and that somewhere along the descending branch of this curve the spherical shape may bifurcate into a pear shape through localized thinning near one of the poles. The bifurcation is associated with the (uniform) surface tension reaching a maximum. It is previously known that whenever a pear-shaped configuration becomes possible, it has lower energy than the co-existing spherical configuration, but the stability of the pear-shaped configuration itself is unknown. With the use of the energy stability criterion, it is shown in this paper that the pear-shaped configuration is unstable under pressure control, but stable under mass control. Our calculations are carried out using the Ogden material model as an example, but it is expected that the qualitative stability results should also be valid for other material models that predict a similar N-shaped behaviour for uniform inflation.

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Section: Introductionmentioning

confidence: 99%

Stability of pear-shaped configurations bifurcated from a pressurized spherical balloon

Fu¹,

Xie²

2014

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

show abstract

“…,i = 0), but the primary stress is non-zero, the incremental heat flux vector simplifies to 10) so that the heat conduction equation (2.7) reduces to…”

Section: Linearised Thermoelastostaticsmentioning

confidence: 99%