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<font 22px/inherit;;inherit;;inherit>**Fluid structure interaction with structural contact **</font>

<font 14px/inherit;;inherit;;inherit>This project introduces a computational tool that performs nonlinear dynamic analysis with positional formulation of fluid-structure interaction (FSI) problems with structural contact. The study of FSI problems with structural contact generates relevant contributions both in engineering (collision problems between immersed solids, floodgates, flow valves and inflatable structures) and in medicine (heart valves and brain aneurysms). A better understanding of these phenomena contributes to the development of treatments and better forms of diagnosis, as well as to the design of artificial valves and reinforcements for repairing aneurysms (stents).</font>

The solution process for the solid is based on Finite Element Method (FEM), while for the fluid it follows the well-established Particle Finite Element Method (PFEM), with both the fluid and structure described within a Lagrangian framework, with time integration performed using the\\
alpha-generalized method. High mesh distortions in the fluid are managed by combining re-meshing with the particle concept at each time step, accommodating significant distortions and topological changes in the fluid domain. Delaunay triangulation generates a convex mesh using the particles as nodes and the α-shape method is employed to remove highly distorted or excessively large elements, as demonstrates as follow:

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Fig. 1 - Hypothetical analysis demonstrating the use of PFEM in an IFE problem.

In addition, there is complexity in enforcing contact conditions and managing fluid discretization in and near the contact region. Structural contact is addressed using a node-to-segment approach based on Lagrange multipliers, with an algorithm to identify the contact occurrence point, as demonstrates as follow:

Fig. 2: Contact problem using node-to-segment approach - (a) Identification of penetration point and (b) Penetration of the slave structure into master structure.

The neo-Hookean constitutive model is employed. Fluid-structure coupling is implemented monolithically, with the current positions serving as the nodal parameters for both fluid and structure.

The following example consists of a tank with a highly flexible gate, fixed at the top, and a barrier at the base that remains undeformed and is instantly released to deform at the beginning of the analysis. The fluid pressure on the left side of the gate forces it into contact with the barrier, as demonstrated below:

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Video 1: A tank with a highly flexible gate in direct contact with a barrier.

This second problem studied the behavior of a simplified aortic valve (two-dimensional approximation) using its symmetry plane, considering only the upper part of the valve with the presence of a single leaflet. Thus, it is allowed for the valve leaflet to undergo the snap-through\\
phenomenon due to pulsatile fluid flow, as demonstrated bellow:

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Video 2: Simplified aortic valve under a pulsatile fluid flow.

Fig 3: Horizontal (a) and vertical (b) displacement of the bottom tip of the leaflet.

The following simulation aims to represent the interaction between both leaflets present in the cardiac aortic valve. A time- and y-coordinate-dependent parabolic inlet velocity profile, in a laminar regime, is prescribed at the left part of the fluid flow.

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Video 3: Heart valve with near leaflets contact.

Fig 4:

This last case is an extension of the previous problem, where the distance between the leaflets is reduced, while keeping the other distances and boundary conditions unchanged. Thus, the structures effectively come into contact, as demonstrated bellow:

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Video 4: Heart valve with effective leaflets contact.

The proposed formulation has proven to be robust and efficient for simulating fluid-structure interaction problems with structural contact, including problems with free fluid surfaces and biomechanical problems, as quantitatively and qualitatively demonstrated by the examples presented.