Many bio and bio-inspired materials are composed of fiber network structures embedded in ground matrices and can be categorized as fibrous biomaterials. Understanding the structure-function relationship of these materials provides insight into the pathophysiology of various diseases, such as arteriosclerosis, and advances many biomedical applications, such as artificial heart valves. Combining numerical methods with experimental technologies is effective for investigating these relationships.

A new computational framework is proposed to simulate the mechanical behavior of fibrous biomaterials. First, the microscopic fiber structure is synthetically generated via a random walk algorithm and incorporated into finite element (FE) simulations based on the embedded fiber approach. The material parameters involved in the generation of these fiber structures have physical or geometric interpretations and can potentially be obtained from experiments. The element residual and stiffness matrix are then derived via a variational approach. Moreover, FE simulations can be easily combined with the Monte Carlo method to consider the material structure randomness and describe the material average behavior. Since the number of degrees of freedom of the discretized system remains unchanged, the proposed framework maintains the computational efficiency of FE simulations while taking into consideration the material microscopic structure.

Poly(ethylene glycol) diacrylate (PEGDA) hydrogel is one bio-inspired material used for tissue engineered heart valves. As an example of applying the proposed framework, various factors including pattern ratio, orientation, and waviness can be numerically investigated for their influence on the mechanical behavior of patterned PEGDA hydrogels. Moreover, a toe-heel-linear stress-strain relationship typically exhibited by biological tissues is depicted by properly tuning the hydrogel properties. Studying these properties provides input for better hydrogel design.

Arterial walls are another example of biological tissues that can effectively use the proposed framework. Structure-function relationships of different arterial wall layers are examined by using layer-specific experimental data. Material structures like fiber dispersion caused by fiber angular distribution and waviness are both considered. Additionally, the material parameters used in the proposed framework can be linked to phenomenological parameters in the homogenized modeling approach. By linking these parameters, it is possible to calculate the phenomenological parameters directly from the quantities measured in experiments.