Analytical and numerical analyses of the micromechanics of soft fibrous connective tissues

State of the art research and treatment of biological tissues require accurate and efficient methods for describing their mechanical properties. Indeed, micromechanics-motivated approaches provide a systematic method for elevating relevant data from the microscopic level to the macroscopic one. In this work, the mechanical responses of hyperelastic tissues with one and two families of collagen fibers are analyzed by application of a new variational estimate accounting for their histology and the behaviors of their constituents. The resulting close-form expressions are used to determine the overall response of the wall of a healthy human coronary artery. To demonstrate the accuracy of the proposed method, these predictions are compared with corresponding 3D finite element simulations of a periodic unit cell of the tissue with two families of fibers. Throughout, the analytical predictions for the highly nonlinear and anisotropic tissue are in agreement with the numerical simulations.