Constrained mixture modeling affects material parameter identification from planar biaxial tests. (July 2019)

• Record Type: Journal Article
• Authors: Maes, Lauranne; Fehervary, Heleen; Vastmans, Julie; Mousavi, S. Jamaleddin; Avril, Stéphane; Famaey, Nele
• Is Part Of: Journal of the mechanical behavior of biomedical materials. Volume 95(2019)
• Page Start: 124
• Page End: 135
• Publication Date: 2019-07
• Subjects: Constrained mixture -- Deposition stretches -- Arterial tissue -- Constitutive modeling -- Parameter estimation; Biomedical materials -- Periodicals; Biomedical materials -- Mechanical properties -- Periodicals; Biomedical materials; Biomedical materials -- Mechanical properties; Periodicals; Electronic journals; 610.28
• DOI: 10.1016/j.jmbbm.2019.03.029
• Languages: English
• ISSNs: 1751-6161

Abstract

Abstract: The constrained mixture theory is an elegant way to incorporate the phenomenon of residual stresses in patient-specific finite element models of arteries. This theory assumes an in vivo reference geometry, obtained from medical imaging, and constituent-specific deposition stretches in the assumed reference state. It allows to model residual stresses and prestretches in arteries without the need for a stress-free reference configuration, most often unknown in patient-specific modeling. A finite element (FE) model requires material parameters, which are classically obtained by fitting the constitutive model to experimental data. The characterization of arterial tissue is often based on planar biaxial test data, to which nonlinear elastic fiber-reinforced material parameters are fitted. However, the introduction of the constrained mixture theory requires an adapted approach to parameter fitting. Therefore, we introduce an iterative fitting method, alternating between nonlinear least squares parameter optimization and an FE prestressing algorithm to obtain the correct constrained mixture material state during the mechanical test. We verify the method based on numerically constructed planar biaxial test data sets, containing ground truth sets of material parameters. The results show that the method converges to the correct parameter sets in just a few iterations. Next, the iterative fitting approach is applied to planar biaxial test data of ovine pulmonary artery tissue. The obtained results demonstrate a convergence towards constrained mixture compatible parameters, which differ significantly from classically obtained parameters. We show that this new modeling approach yields in vivo wall stresses similar to when using classically obtained parameters. However, due to the numerous advantages of constrained mixture modeling, our fitting method is relevant to obtain compatible material parameters, that may not be confused with parameters obtained in a classical way.