ABSTRACT

In this talk, we focus on the modeling, numerical analysis, and simulation of large-strain (hyperelastic) elasticity problems, with particular application to the study of soft biological tissues. We also consider frictional contact between two hyperelastic bodies, with application to the deployment of a stent in an arterial tissue. For the numerical approximation, the key idea is to design a time integration scheme consistent with the energy of the system at the discrete level: that is, conserving energy in the frictionless contact case, and such that no numerical dissipation is introduced in the frictional and, possibly, viscosity cases. The numerical approximation of frictional contact is achieved using a Primal–Dual Active Set method, without the need to introduce Lagrange multipliers. Numerical simulations are performed on academic and real-world scenarios; in particular, the latter concerns the representation of the deployment by contact of a stainless steel stent in an arterial tissue. This is a joint work with Mikaël Barboteu, Serge Dumont, and Christina Mahmoud.

SPEAKER

Dr. Francesco Bonaldi is an Associate Professor (Maître de Conférences) of Applied Mathematics at the University of Perpignan, specializing in theoretical and numerical aspects of Continuum Mechanics. His research spans topics including energy-preserving schemes for dynamic nonlinear elasticity, contact mechanics, polytopal exterior calculus, discrete De Rham complexes, and two-phase flow in fractured porous media with mechanical coupling. His academic path includes postdoctoral positions at leading institutions: IMAG Montpellier, Inria Sophia Antipolis & Université Côte d’Azur, and MOX Politecnico di Milano, where he developed high-order methods and advanced discontinuous Galerkin techniques for complex wave propagation and plate mechanics. He earned his Ph.D. at IMAG Montpellier, focusing on robust asymptotic methods in mechanics simulations under the ANR project ARAMIS and supervised by Giuseppe Geymonat (Ecole Polytechnique), Françoise Krasucki (University of Montpellier), and Marina Vidrascu (Inria Paris). He recently obtained a research grant by ANR for the four-year project MaNStarT – Mathematical, mechanical, and numerical modeling of stents in arterial tissues.