This study examines how fiber-matrix invariant coupling influences the prediction of limit-point instability. Such behavior commonly occurs in heart and bladder and is closely linked to cardiovascular mechanics, particularly the formation of aortic aneurysms. Prior studies have utilized a well-known limiting chain-extensibility parameter to establish configuration-dependent stability thresholds for Gent materials (e.g., \(J_m < 18.2\) for isotropic tubes and \(J_m = 0.1\) for anisotropic tubes), but no corresponding thresholds exist for finitely extensible spherical shells. Certain assumptions, such as incompressibility, thin-wall kinematics, and closed-end inflation, give rise to these stability criteria, which are not universal. This work primarily aims to identify configuration-dependent stability thresholds for isotropic and anisotropic biological spheres under inflation and to assess how these configuration-dependent 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 ( \(\alpha , \beta \) ). The formulation yields a closed-form pressure-stretch relation that generalizes existing uncoupled models and enables systematic identification of instability thresholds. The onset of instability is heavily influenced by the fiber orientations, invariant coupling exponents, and the associated threshold values of the chain extensibility parameter. By comparing isotropic and anisotropic modes with and without fiber-matrix coupling, the impact of these essential characteristics on the inflation mechanics of finitely extensible biological spherical shell is investigated. Test data from a pressurized monkey bladder is used to compare the model predictions.
