A micromechanics finite-strain constitutive model of fibrous tissue

Abstract

Biological tissues have unique mechanical properties due to the wavy fibrous collagen and elastin microstructure. In inflation, a vessel easily distends under low pressure but becomes stiffer when the fibers are straightened to take up the load. The current microstructural models of blood vessels assume affine deformation; i.e., the deformation of each fiber is assumed to be identical to the macroscopic deformation of the tissue. This uniform-field (UF) assumption leads to the macroscopic (or effective) strain energy of the tissue that is the volumetric sum of the contributions of the tissue components. Here, a micromechanics-based constitutive model of fibrous tissue is developed to remove the affine assumption and to take into consideration the heterogeneous interactions between the fibers and the ground substance. The development is based on the framework of a recently developed second-order homogenization theory, and takes into account the waviness, orientations, and spatial distribution of the fibers, as well as the material nonlinearity at finite-strain deformation. In an illustrative simulation, the predictions of the macroscopic stress-strain relation, and the statistical deformation of the fibers are compared to the UF model, as well as finite-element (FE) simulation. Our predictions agree well with the FE results, while the UF predictions significantly overestimate. The effects of fiber distribution and waviness on the macroscopic stress-strain relation are also investigated. The present mathematical model may serves as a foundation for native as well as for engineered tissues and biomaterials.

A validated 3D microstructure-based constitutive model of coronary artery adventitia

“…Mechanical predictions are thought to be more accurate than those of phenomenological models, as these models account for microstructural features of vessel components, as well as heterogeneity of material properties. The microstructural parameters have been ad hoc rather than based on experimental measurements, due to limited morphological data of the vessel wall (4,17,23,51). The microstructure of the vessel wall, which includes elastin and collagen fibers, smooth muscle cells, and ground substance, is distributed differently in individual vessel layers, i.e., tunica media and adventitia (8,36,43).…”

Determination and Finite Element Validation of the WYPIWYG Strain Energy of Superficial Fascia from Experimental Data

“…[13,28]) and non-affine models (e.g. [29,30]). The last ones emphasize the fact that the stress and strain fields are different for the components and then contradict the assumption made in affine models.…”

Fluid-Structure Interaction Model of Aortic Valve With Porcine-Specific Collagen Fiber Alignment in the Cusps

“…The finite strain theory was employed since it allows arbitrarily large deformations and it is suitable for modeling biological soft tissue [22]. The equilibrium equations were solved by Newton's method.…”