Explicit consideration of fiber recruitment in vascular constitutive formulation using beta functions

• Published in: Journal of the mechanics and physics of solids Vol. 163; p. 104837
• Main Authors: He, Xuehuan, Lu, Jia
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 01.06.2022; Elsevier BV
• Subjects: Aneurysms; Aorta; Beta functions; Collagen fiber; Constitutive models; Dispersion; Mathematical models; Mechanical properties; Polynomials; Probability distribution functions; Recruitment; Vascular tissue; Vascular tissues; Waviness; Beta functions; Vascular tissues; Collagen fiber; Waviness; Dispersion; Recruitment
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2022.104837

Constitutive models are of fundamental importance for describing the mechanical behavior of vascular tissues. In this article, we present a constitutive model that explicitly accounts for collagen fiber recruitment. The formulation, developed based two experimental observations, consists in a systematic use of beta functions. The distribution of random waviness is modeled by beta distribution, and the fiber stresses are represented by incomplete beta functions which are shown to be flexible in capturing different types of responses data. A four-point dispersion model, derived in the context of planar von Mises distribution, is developed to take into account of the orientation distribution of fibers. The dispersion weights appear as Bernstein polynomials of a single dispersion parameter. The descriptive and predictive capabilities are assessed using three groups of experimental data encompassing the responses of porcine thoracic aorta, human intracranial aneurysm, and human ascending thoracic aortic aneurysm tissues. The descriptive performance is evaluated by the quality of constitutive fitting. The predictive ability is tested based on the accuracy in predicting unfitted responses as well as in finite element simulations. The assessment indicates that the model has excellent descriptive and predictive capabilities. •The constitutive equations are given in closed-form, represented by incomplete beta functions.•The representation is derived systematically from two experimental observations.•Collagen fiber recruitment is explicitly considered.•All constitutive parameters have physical meaning.•A four-point algorithm is developed to deal with angular dispersion of fibers.•The model demonstrates excellent descriptive and predictive capabilities.