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When a specimen of non-trivial shape undergoes deformation under a dead load or during an active process, finite element simulations are the only technique for evaluating the deformation. Classical books describe complicated techniques for evaluating stresses and strains in semi-infinite, circular or cylindrical objects. However, the results obtained are limited, and it is well known that elasticity (linear or nonlinear) is strongly intertwined with geometry. For the simplest geometries, it is possible to determine the exact deformation, essentially for low loading values, and prove that there is a threshold above which the specimen loses stability. The next step is to apply perturbation techniques (linear and nonlinear bifurcation theory).
In this talk, I will demonstrate how many aspects can be simplified or revealed through the use of complex analysis and conformal mapping techniques for shapes, strains, and active stresses in thin samples. Examples include leaves and embryonic jellyfish.
Further Information
Professor Martine Ben Amar is a theoretical physicist whose work explores the physics and mechanics of soft matter, with applications ranging from fundamental instabilities in solids and fluids to biological growth processes. Her research has addressed phenomena such as dendritic growth, Saffman–Taylor instability, elastic singularities, and morphogenesis in vegetal and animal tissues. More recently, she has focused on the interface between physics and biology, modelling the growth of cancerous tumours through reaction–diffusion equations and studying the role of mechanical stresses in tissue development—work that connects directly with medical applications in collaboration with clinicians.
A graduate in atomic physics, she has taught at UPMC since 1993 and was elected a senior member of the Institut Universitaire de France in 2011. She held the McCarthy Chair at MIT in 1999–2000 and has led the federation Dynamics of Complex Systems, uniting over 200 researchers across Paris institutions. Passionate about science, she describes her vocation as “understanding, showing, and predicting the laws of the universe and life.”