Pjg Piet Schreurs

A three-dimensional computational analysis of fluid–structure interaction in the aortic valve

Numerical analysis of the aortic valve has mainly been focused on the closing behaviour during the diastolic phase rather than the kinematic opening and closing behaviour during the systolic phase of the cardiac cycle. Moreover, the fluid-structure interaction in the aortic valve system is most frequently ignored in numerical modelling. The effect of this interaction on the valves behaviour during systolic functioning is investigated. The large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modelling. This has impeded numerical analyses of valves operating under physiological conditions. A numerical method, known as the Lagrange multiplier based fictitious domain method, is used to describe the large leaflet motion within the computational fluid domain. This method is applied to a three-dimensional finite element model of a stented aortic valve. The model provides both the mechanical behaviour of the valve and the blood flow through it. Results show that during systole the leaflets of the stented valve appear to be moving with the fluid in an essentially kinematical process governed by the fluid motion.

Overall behaviour of heterogeneous elastoviscoplastic materials: effect of microstructural modelling

Homogenisation methods provide an efficient way to model the mechanical behaviour of heterogeneous materials. In this paper, a homogenisation procedure is adopted that allows to determine apparent properties for Perzynas elastoviscoplastic constitutive law for arbitrary microstructures. Numerical simulations on a representative volume element (RVE) are performed, from which the volume averaged state variables are acquired, necessary to establish the constitutive equations for the equivalent homogeneous medium. The applicability of mixed and periodic boundary conditions has been assessed. In addition, the difference between uniform and irregular distributions of the microstructural constituents is discussed. To substantiate our findings, a comparison is made between the global response of a heterogeneous and the corresponding homogenised structure.

A two-dimensional fluid–structure interaction model of the aortic value

Failure of synthetic heart valves is usually caused by tearing and calcification of the leaflets. Leaflet fiber-reinforcement increases the durability of these valves by unloading the delicate parts of the leaflets, maintaining their physiological functioning. The interaction of the valve with the surrounding fluid is essential when analyzing its functioning. However, the large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modeling. This has, so far, obstructed numerical analyses of valves operating under physiological conditions. A two-dimensional fluid-structure interaction model is presented, which allows the Reynolds number to be within the physiological range, using a fictitious domain method based on Lagrange multipliers to couple the two phases. The extension to the three-dimensional case is straightforward. The model has been validated experimentally using laser Doppler anemometry for measuring the fluid flow and digitized high-speed video recordings to visualize the leaflet motion in corresponding geometries. Results show that both the fluid and leaflet behaviour are well predicted for different leaflet thicknesses.

Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole

The effect of collagen fibers on the mechanics and hemodynamics of a trileaflet aortic valve contained in a rigid aortic root is investigated in a numerical analysis of the systolic phase. Collagen fibers are known to reduce stresses in the leaflets during diastole, but their role during systole has not been investigated in detail yet. It is demonstrated that also during systole these fibers substantially reduce stresses in the leaflets and provide smoother opening and closing. Compared to isotropic leaflets, collagen reinforcement reduces the fluttering motion of the leaflets. Due to the exponential stress-strain behavior of collagen, the fibers have little influence on the initial phase of the valve opening, which occurs at low strains, and therefore have little impact on the transvalvular pressure drop.

Simulation of forming processes, using the arbitrary Eulerian Lagrangian formulation

The finite element method is frequently used to simulate forming processes for the purpose of predicting the quality of the final product and the load on the tool. If the method is based on either the Eulerian or the Lagrangian formulation, some simulations are arduous or even impossible. To avoid this the arbitrary Eulerian-Lagrangian (AEL) formulation can be used. In this paper the theoretical background of this formulation is presented and some new concepts are introduced. The formulation offers the possibility to improve the geometry of distorted elements. A procedure for automatic mesh adaptation is described. The formulation is employed in the simulation of some axisymmetric forming processes.

A three-dimensional mechanical analysis of a stentless fibre-reinforced aortic valve prosthesis.

Failure of bioprosthetic and synthetic three-leaflet valves has been shown to occur as a consequence of high tensile and bending stresses, acting on the leaflets during opening and closing. Moreover, in the stented prostheses, whether synthetic or biological, the absence of contraction of the aortic base, due to the rigid stent, causes the leaflets to be subjected to an unphysiological degree of flexure, which is related to calcification. It is shown that the absence of the stent, which gives a flexible aortic base and leaflet attachment, and leaflet fibre-reinforcement result in reduced stresses in the weaker parts of the leaflets in their closed configuration. It is postulated that this leads to a decrease of tears and perforations, which may result in a improved long-term behaviour. The effect of a flexible leaflet attachment and aortic base of a synthetic valve is investigated with a finite element model. Different fibre-reinforced structures are analysed with respect to the stresses that are likely to contribute to the failure of fibre-reinforced prostheses and compared with the results obtained for a stented prosthesis. Results show that for the stentless models a reduction of stresses up to 75% is obtained with respect to stented models with the same type of reinforcement.

A continuum approach to brittle and fatigue damage : theory and numerical procedures

A unified continuum approach to brittle and fatigue damage is presented. A scalar variable is used to represent the damage state. General forms of the constitutive equations are established on a thermodynamic basis. Specific evolution laws are postulated and used to illustrate the capacity of the model. The governing equations are solved numerically. The computational effort is reduced by the application of an adaptive stepsize selection procedure for the integration of the rate equations and by uncoupling the constitutive equations. The response of a plate with an induced crack subjected to periodic loading is studied.

A three-dimensional analysis of a fibre-reinforced aortic valve prosthesis

Failure of synthetic heart valves is usually caused by tearing and calcification of the leaflets. It is postulated that leaflet fibre-reinforcement leads to a decrease of tears and perforations as a result of reduced stresses in the weaker parts of the leaflets. A three-dimensional finite element model of a reinforced three-leaflet valve prosthesis was developed to analyse the stress reduction. Different fibre reinforcements were investigated and the model responses were analysed for stresses that are expected to contribute to failure of fibre-reinforced valve prostheses. Results of these simulations show that, in peak stress areas of reinforced models, up to 60% of the maximum principal stresses is taken over by fibres and that, in some cases of reinforcement, a more homogeneous stress distribution is obtained.

Homogenisation of structured elastoviscoplastic solids at finite strains

Abstract Studying the relation between microstructural phenomena and the macroscopic behaviour will provide a way to design the microstructure of a material such that specific requirements on the resulting macroscopic mechanical behaviour can be fulfilled. One way to obtain a quantitative relation between the separate scales is to use homogenisation methods. A numerical homogenisation method has been developed to model the mechanical behaviour of heterogeneous elastoviscoplastic solids at finite strains. The thus obtained constitutive equation enables the modelling of complex macrostructures, while taking into account the influence of the microstructure. The method has been validated by comparing results of homogenised simulations with reference solutions. For this purpose, a specimen with a periodic microstructure and an irregular microstructure has been considered.The continuous matrix material is assumed to be polycarbonate, whereas the heterogeneities are taken to be rubber particles and voids.

An experimental and numerical study of the wall ironing process of polymer coated sheet metal

In the traditional manufacturing process for metal food and beverage containers, a food contact-safe lacquer is sprayed onto the can before filling. This time consuming and therefore expensive process can be eliminated using a polymer coated sheet metal provided that the polymer will survive the manufacturing operations. The most critical stage in can making is the ironing process because of the large deformations that occur. This paper presents experimental and numerical results regarding the ironing process of polymer coated aluminium and polymer coated steel. A plane strain strip ironing device has been constructed to investigate the influence of the ironing reduction, velocity and die angle on the process forces and friction. Furthermore, an in-situ study of the displacement and strain fields has been performed in the strip ironing experiments using a digital image correlation technique. Simulations of the process have been performed using an arbitrary Lagrange Euler method based on an operator splitting procedure (OS-ALE). The constitutive behaviour of metal and polymer has been modelled with a generalised compressible Leonov model with a Bodner–Partom and an Eyring viscosity function, respectively. The experimental results are in good agreement with numerical simulations.