x 0.4 mm (Fig. 1). Four evenly spaced node forces, with 5 mm between two adjacent nodes and 2.5 mm inside the specimen edge, were imposed on each side (Fig. 1). Each node force was 2.5 N, imposing a net total of 1 MPa Lagrangian stress on each edge. Similar to the actual experimental biaxial testing setup 19, only the central region of the specimen was considered for stress–strain measurements. This was accomplished by averaging the stress and strain tensor components for sixteen elements located in the center of the FE model, delimiting a 5 mm x 5 mm region. Figure 1 - (a) Diagram of a biaxial test specimen and (b) simulated biaxial test specimen stress distribution at peak load. BHV Finite Element Model The BHV finite element model was developed previously by Sun et al. 14 (Fig. 2). Briefly, tri-leaflet BHVs are fabricated from GLBP sheets that are die-cut to form leaflets, which are then mounted onto a metal stent. In the finite element model the stent was constructed using beam elements. The wireframe was assigned a Young’s modulus of 2.33x107 kPa and a Poisson ratio of 0.3. The leaflets were attached to the valve stent and modeled using large strain brick elements. Each leaflet had its own local coordinate system for material property definitions that are fully defined by the constitutive law, Eq. (3), and incorporated into the user subroutine UMAT. Details of the constitutive model implementation into ABAQUS have been previously presented 18,20. It was assumed that each leaflet can be modeled with one set of material parameters, which was supported by experimental findings 14. The contact between two leaflets was modeled using a master-slave contact pair (an option in ABAQUS). The leaflet that was stiffer in the radial direction was assigned as the master surface while the other was specified as the slave surface. A quasi-static approach was used to analyze the deformation of the model from a stress-free position to a fully loaded configuration by applying a uniform pressure to the aortic side of the leaflet (Fig. 2). FE Parametric Analysis T11 T22 x1 x2 a. b. Undeformed valve Deformed valve Valve stent Figure 2 – An overlay plot of undeformed and deformed valve finite element models, showing stress distribution of Maximum Principal Stress under a valve closing pressure of 120 mmHg. 75
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