Role of fiber-matrix coupling on limit point instability in pressurized finitely extensible biological tube

This article addresses the critical role of fiber-matrix invariant coupling in accurately predicting the loss of stability, characterized by a non-monotonic relationship between the inflation-extension response of a thin-walled biological tube, often referred to as limit-point instability. Such deformations frequently occur in arteries and veins and are particularly relevant to cardiovascular mechanics, especially in aneurysm formation. Prior research used the chain extensibility parameter to establish the configuration-dependent stability thresholds for Gent materials (e.g., J m < 18.2 for thin-walled isotropic membranes and J m = 0.1 for anisotropic tubes under uniform inflation). These thresholds are not universal and arise under specific assumptions, such as incompressibility, thinwall kinematics, and closed-end inflation. This work aims to evaluate further how these configuration-specific thresholds shift when fiber-matrix invariant coupling is incorporated. The strain energy density is formulated as a function of the invariants I 1 (matrix) and I 4 (fiber), incorporating nonlinear coupling exponents (α, β). The onset of instability is heavily influenced by the fiber orientations, invariant coupling exponents, and the associated threshold values of the chain extensibility parameter. The impact of these critical parameters on the mechanical response of a pressurized finitely extensible biological tube is illustrated by comparing anisotropic modes to isotropic modes, with and without fiber-matrix coupling effects. The modeling results are validated against pressurized porcine artery sample datasets.