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Complex analysis and nonlinear elasticity: the Biot instability revisited.

Presented by: 
Martine Ben Amar
Monday 28th October 2019 - 10:00 to 11:00
INI Seminar Room 1
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.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons