Anisotropic Soft Composite Based Hyperelastic Model

Abstract

Tissues and organs are soft composite systems made of collagen fibers embedded within an extracellular matrix. These soft composite systems exhibit directional and regional material anisotropy due to varying fiber distributions and orientations. To date, anisotropic material properties of soft composite systems have been characterized using simplified isotropic and transversely isotropic hyperelastic material models in various computational and experimental studies. These simplifications may not only lead to inaccurate results from analyses, but also inhibit the study of the effect of important tissue modifications due to disease. In this work, a novel composite based hyperelastic model was developed which can characterize tissue anisotropy. This model considers both the soft fibers and matrix to be hyperelastic materials, which interact through shear deformation. The effect of the individual contribution of the fibers and matrix were introduced into the numerical framework for a single soft composite layer and the changes due to variations in the fiber orientation were incorporated into the strain energy functions. Also, strain energy formulations were developed for multiple soft composite layers with varying fiber orientations and contributions, which can describe the biomechanical behavior of organs consisting of multiple tissue layers. Stress versus 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 loads in literature were characterized using the novel anisotropic hyperelastic model. An average R2 correlation index of 0.983 was estimated for the developed model. To date, such a robust anisotropic hyperelastic model has not been developed to the best of our knowledge, which would be indispensable for experimental characterization of tissues and for improving the fidelity of computational models of organ systems in future.