A Physically-Based Anisotropic Discrete Fiber Model for Fibrous Soft Tissues

Abstract

Physically-based fibrous soft tissue models often consider the tissue to be a collection of fibers with a continuous distribution function to represent their orientations. This study proposes a simple model for the response of fibrous connective tissues in terms of a discrete number of fiber bundles. The proposed model consists of six weighted fiber bundles orientated such that they pass through opposing vertices of an icosahedron. A novel aspect of the proposed model is the use of a simple analytical function to represent the undulation distribution of the collagen fibers. The mechanical response of the elastin fiber is represented by a neo-Hookean hyperelastic equation. A parameter study was performed to analyze the effect of each parameter on the overall response of the model. The proposed model accurately simulated the uniaxial stretching of pig skin with an 8% error-of-fit for stretch ratios up to 1.8. The model also accurately simulated the biaxial stretching of rabbit skin with a 10% error-of-fit for stretch ratios up to 1.9. The stiffness of the collagen fibers determined by the model was about 100 MPa for the rabbit skin and 900 MPa for the pig skin, which are comparable with values reported in the literature. The stiffness of the elastin fibers in the model was about 2 kPa.