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Vendredi 22 Juin 2018 / IRPHE

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Séminaire régulier IRPHE

Into the crease : nucleation of a discontinuous solution in nonlinear elasticity

Orateur : Pasquale Ciarletta
MOX Laboratory, Dept. of Mathematics, Politecnico di Milano, Italy. CNRS, Sorbonne Universités, UMR7190, Paris, France.

Abstract  : Discontinuous solutions, such as cracks or cavities, can suddenly appear in elastic solids when a limiting physical condition is attained. Similarly, self-contacting folds can nucleate at a free surface of a soft material when subjected to a critical compression. Unlike other elastic instabilities, such as buckling and wrinkling, the onset of creasing is invisible to linearization techniques. Understanding the nucleation of such a localised solution has been a formidable mathematical challenge that remained elusive for over a century.

In this talk, I will discuss some recent analytic insights solving the quest for both the nucleation threshold and the emerging crease morphology. Firstly, I will show that creasing is a material instability, meaning that it is local in the physical space and global in the configurational sense. I will present an original mathematical approach circumventing the difficulties of calculus of variations, giving the first theoretical prediction of the crease nucleation threshold as the limiting condition for the loss of a strong local minimum. Secondly, I will derive the analytic prediction for the incipient crease morphology by solving a singular boundary value problem in nonlinear elasticity. Notably, I will show with patched asymptotic techniques that the self-contacting crease acts like the point-wise disturbance in the Oseen’s correction for the Stokes flow past a circle.

The analytic predictions are in very good agreement with experimental and numerical data. They prove fundamental insights either for understanding the creasing onset in living matter, e.g. brain convolutions, or for pushing innovation in digital fabrication, e.g. 4D printing and morphable meta-materials.

Date et lieu : le vendredi 22 juin à 14h00, salle de séminaires IRPHE

Voir en ligne : la page personnelle de l’orateur