Soft composite based hyperelastic model for anisotropic tissue characterization

Soft tissues are complex anisotropic composite systems comprising of multiple differently oriented layers of fiber embedded within a soft matrix. To date, soft tissues have been mainly characterized using simplified linear elastic material models, isotropic viscoelastic and hyperelastic models, and transversely isotropic models. In such models, the effect of fiber volume fraction (FVF), fiber orientation, and fiber-matrix interactions are missing, inhibiting accurate characterization of anisotropic tissue properties. The current work addresses this literature gap with the development of a novel soft composite based material framework to model tissue anisotropy. In this model, the fiber and matrix are considered as separate hyperelastic materials, and fiber-matrix interaction is modeled using multiplicative decomposition of the deformation gradient. The effect of the individual contribution of the fibers and matrix are introduced into the numerical framework for a single soft composite layer, and fiber orientation effects are incorporated into the strain energy functions. Also, strain energy formulations are developed for multiple soft composite layers with varying fiber orientations and contributions, describing the biomechanical behavior of an entire anisotropic tissue block. Stress-strain relationships were derived from the strain energy equations for a uniaxial mechanical test condition. To validate the model parameters, experimental models of soft composites tested under uniaxial tension were characterized using the novel anisotropic hyperelastic model (R-2 = 0.983). To date, such a robust anisotropic hyperelastic composite framework has not been developed, which would be indispensable for experimental characterization of tissues and for improving the fidelity of computational biological models in future.