Development of an improved parameter fitting method for planar biaxial testing using rakes

Abstract

A correct estimation of the material parameters from a planar biaxial test is crucial since they will affect the outcome of the finite element model in which they are used. In a virtual planar biaxial experiment, a difference can be noticed in the stress calculated from the force measured experimentally at the rakes and the actual stress at the center of the sample. As a consequence, a classic parameter fitting does not result in a correct estimation of the material parameters. This difference is caused by the boundary conditions of the set‐up and is among others dependent on the sample material. To overcome this problem, a new parameter fitting procedure is proposed that takes this difference into account by calculating a finite element–based correction vector. This paper describes the methodology to apply this new parameter fitting procedure on real experimental data from a planar biaxial test using rakes. To this end, image processing is used to extract the experiment characteristics. This information is used to construct a finite element model. Two variations of the new parameter fitting procedure are investigated using two human aortic samples: a basic approach and an image‐based approach. The performance of the method is assessed by the difference between the force measured at the rakes during the experiment and the force at the rakes obtained from the finite element simulation. Both approaches of the new parameter fitting procedure lead to an improved estimation of the sample behavior compared with the classic approach.

A detailed mechanical and microstructural analysis of ovine tricuspid valve leaflets

“…However, as per Saint Vernant's principle, we analyzed strain in the sample center, away from the boundaries. While others have accounted for the boundary effects due to the rake insertions, we found that the small reported error accrued by ignoring such effects are negligible in comparison to the intersubject variations that we observed in our study [59].…”

An improved parameter fitting approach of a planar biaxial test including the experimental prestretch

“…A boundary condition corrected parameter fitting approach (BCC(p)) proposed by Fehervary et al can also be performed [18]. Unlike the classical fittings, this iterative method accounts for the difference between the force measured experimentally at the rakes and the force calculated from the stress present at the center of the sample.…”

“…To overcome this, studies have been conducted to gain more insight in various aspects of the experimental protocol and data analysis. The influence of the gripping mechanism and placement on different sample shapes has been studied [12,13,15,16,17,18], as well as other aspects of the protocol such as the effect of preconditioning [19,20], the effect of flattening an excised sample prior to sample mounting [21], the difference between a force-and displacement-based protocol, the sample side on which the deformation is tracked [14] and the variations of the experimental stress calculation and parameter fitting [12].…”

“…One thing that is frequently overlooked is the correct definition of the stressfree reference situation. Typically, after the sample dimensions are defined in its unloaded, excised state, the sample is mounted on a planar biaxial tensile device and a preload is applied to avoid sagging [18]. Hence, the sample state at the start of the loading cycle, during which a predefined force or displacement is successively imposed and released, is already loaded and considerably differing from the unloaded state.…”

“…Hence, the sample state at the start of the loading cycle, during which a predefined force or displacement is successively imposed and released, is already loaded and considerably differing from the unloaded state. Nonetheless, the preloaded configuration is often held as the reference state, while the consequence of this assumption is either neglected or, in some cases, acknowledged but falling outside the scope of the study [18,22]. Referencing a prestretched, loaded state can lead to an underestimation of the tissue's compliance, especially for tissues exhibiting a low stiffness close to their zero stress state [19,23].…”