E. Rosset | Searcharxiv

arXiv2024

Stable determination of the Winkler subgrade coefficient in a nanoplate

We study the inverse problem of determining the Winkler coefficient in a nanoplate resting on an elastic foundation and clamped at the boundary. The nanoplate is described within a simplified strain gradient elasticity theory for isotropic materials, under the Kirchhoff-Love kinematic assumptions in infinitesimal deformation. We prove a global H\"older stability estimate of the subgrade coefficient by performing a single interior measurement of the transverse deflection of the nanoplate induced by a load concentrated at one point.

math.AP↗

arXiv2019

Model reduction methodology for computational simulations of endovascular repair

Endovascular aneurysm repair (EVAR) is a current alternative treatment for thoracic and abdominal aortic aneurysms, but is still sometimes compromised by possible complications such as device migration or endoleaks. In order to assist clinicians in preventing these complications, finite element analysis (FEA) is a promising tool. However, the strong material and geometrical nonlinearities added to the complex multiple contacts result in costly finite-element models. To reduce this computational cost, we establish here an alternative and systematic methodology to simplify the computational simulations of stent-grafts (SG) based on FEA. The model reduction methodology relies on equivalent shell models with appropriate geometrical and mechanical parameters. It simplifies significantly the contact interactions but still shows very good agreement with a complete reference finite-element model. Finally, the computational time for EVAR simulations is reduced of a factor 6 to 10. An application is shown for the deployment of a SG during thoracic endovascular repair, showing that the developed methodology is both effective and accurate to determine the final position of the deployed SG inside the aneurysm.

physics.med-ph↗