A primal-dual active set method for superelasticity, finite-strain elastoplasticity, and contact: application to modeling of stent devices
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We devise a mathematical and numerical model of superelastic and finite-strain elastoplastic problems, with application to stent devices deployed in soft biological tissues, thereby extending the work in (Barboteu et al., Computer Methods in Applied Mechanics and Engineering, 2024) where a pure hyper-viscoelastic behavior of two deformable bodies in contact is addressed. After presenting the general setting of the problem, with suitable constitutive assumptions, we provide an energy-consistent numerical approximation thereof, in adequacy with the continuous framework. A physical dissipation of mechanical energy is expected, because of the superelastic and plastic behaviors. More particularly, we are interested in the numerical simulation of such non-smooth and non-linear problems based on employing a Primal--Dual Active Set (PDAS) approach. One of the main assets of the proposed algorithm is that it does not require the usage of Lagrange multipliers to impose the active/inactive constraints. We validate the method by comparing it with classical radial return mapping strategies, and test the numerical scheme on academic and real-life scenarios, the latter representing the deployment of a superelastic (such as nitinol) or elastoplastic (such as stainless-steel or silicone) stent in an arterial tissue.
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