Complex analysis and nonlinear elasticity: the Biot instability revisited.

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• Martine Ben Amar (CNRS - Ecole Normale Superieure Paris; Université Pierre et Marie Curie Paris)
• Monday 28 October 2019, 10:00-11:00
• Seminar Room 1, Newton Institute.

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CATW02 - Complex analysis in mathematical physics and applications

The Biot instability is probably the most useful tool to explain many features in morphogenesis of soft tissues. It explains pretty well the circumvolutions of the brain, the villi of our intestine or our fingerprints. Nevertheless, the theory remains technically difficult for two main reasons: the constraint of incompressibility but also the geometry of finite samples. For the simplest case, that is the semi-infinite Neo-Hookean sample under growth or compression, I will show that complex analysis offers a simple way to treat the buckling instability at the Biot threshold,but also above and below the threshold.

This talk is part of the Isaac Newton Institute Seminar Series series.

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