Abstract
The elastic behavior of arteries is nonlinear when subjected to large deformations. In order to measure their anisotropic behavior, planar biaxial tests are often used. Typically, hooks are attached along the borders of a square sample of arterial tissue. Cruciform samples clamped with grips can also be used. The current debate on the effect of different biaxial test boundary conditions revolves around the uniformity of the stress distribution in the center of the specimen. Uniaxial tests are also commonly used due to simplicity of data analysis, but their capability to fully describe the in vivo behavior of a tissue remains to be proven. In this study, we demonstrate the use of inverse modeling to fit the material properties by taking into account the non-uniform stress distribution, and discuss the differences between the three types of tests. Square and cruciform samples were dissected from pig aortas and tested equi-biaxially. Rectangular samples were used in uniaxial testing as well. On the square samples, forces were applied on each side of edge sample attached with hooks, and strains were measured in the center using optical tracking of ink dots. On the cruciform and rectangular samples, displacements were applied on grip clamps and forces were measured on the clamps. Each type of experiment was simulated with the finite element method. The parameters of the Mooney-Rivlin constitutive model were adjusted with an optimization algorithm so that the simulation predictions fitted the experimental results. Higher stretch ratios (>1.5) were reached in the cruciform and rectangular samples than in the square samples before failure. Therefore, the nonlinear behavior of the tissue in large deformations was better captured by the cruciform biaxial test and the uniaxial test, than by the square biaxial test. Advantages of cruciform samples over square samples include: 1) higher deformation range; 2) simpler data acquisition and 3) easier attachment of sample. However, the nonuniform stress distribution in cruciform samples requires the use of inverse modeling adjustment of constitutive model parameters.
Highlights
Due to the difficulty of testing soft tissues such as arteries in vivo, mechanical testing of arteries in vitro is often preferred
Because inverse modeling can take into account the well-defined boundary conditions of biaxial cruciform samples, the main objective of this study is to evaluate the feasibility of inverse modeling for biaxial testing of cruciform samples over a wider range of strains than is possible with square samples
For the uniaxial rectangular and the biaxial cruciform samples, the nominal stretch ratio was calculated using the distance between the grips
Summary
Due to the difficulty of testing soft tissues such as arteries in vivo, mechanical testing of arteries in vitro is often preferred. According to the Saint-Venant principle, stress distribution in a body is uniform away from the points of application of the load This implies that local stress concentration phenomena occur close to the point of application of the load (edges of the sample), depending on the way the load is applied. Strain is typically measured far from the edges of the sample This approach has been demonstrated both on uniaxial [4]-[6] and biaxial experiments [7]-[15]. Cruciform samples clamped with grips are often used for testing industrial materials when sample thickness distribution can be controlled [20] [21] This type of sample geometry creates high stresses in the curved parts of the sample boundaries, as is demonstrated with computer simulations on various biaxial sample shapes and boundary conditions [22]
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