Titre

Abstract: 

This work focuses on the simulation of shear wave propagation in the cornea. The underlying application is the detection, through elastography techniques, of pathologies associated with changes in tissue mechanics. Reproducing transient elastography poses several mechanical and numerical challenges. Intraocular pressure induces a nonlinear problem, while the nearly incompressible behavior of the cornea leads to numerical locking and stability issues for explicit schemes. Moreover, the model is three-dimensional and anisotropic, making computational efficiency critical.

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The governing equations of the problem are initially derived by linearization: a non-linear elastostatic problem yielding the inflated configuration of the cornea and a linearized wave propagation problem. For the latter, we develop a second-order, energy preserving and fully explicit numerical scheme in order to deal with limitations associated to nearly-incompressibility. The method combines high-order spatial discretization with a stabilized explicit time integration strategy.

Finally, we extend the numerical framework to the full nonlinear elastodynamic problem. To preserve the computational efficiency of explicit time integration with finite element discretization, we adopt the pseudo-energy conserving scheme of Marazzato et al. (2020) developed for Hamiltonian dynamics. The scheme is second-order, explicit and based on adaptive time-stepping to control the discrete energy.

‼️ Le séminaire peut être suivi en ligne via le lien : https://univ-amu-fr.zoom.us/j/95011527683?pwd=bTeNvaaZY75buaa7bRL0pcucXSASm7.1

Le mardi 15 septembre 2026 à 11h00 / Amphithéâtre François Canac, LMA

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