This study investigates a filament-wound tube model incorporating fiber undulation from the filament winding process. The model was analyzed using the finite element method in the linear regime, then compared with the shell model and radial crushing experiment. Results showed that the solid model predicts the radial compression stiffness with a higher level of accuracy than the shell model due to the inclusion of the fiber undulation feature. This model is a first step towards the development of a composite pressure vessel model where fiber undulation is more frequent, and also for predicting failure initiation and damage propagation.

Collagen, the most abundant protein in the human body, plays a pivotal role in the functioning of tissues such as cartilage of synovial joints. Mathematical modeling enables the more detailed study of the physical behavior of the network under load bearing. In this study, we aimed to develop a microscopic finite element (FE) modeling approach for the study of the stresses and strains of the collagen fibrils of cartilage under mechanical loading. This new approach enabled the two-dimensional modeling of a series of collagen meshwork at the microscopic level based on typical superficial collagen fibril structures of the articular cartilage. A collagen fibril network, a microscopic structure composed of 24 collagen fibrils, was designed to mimic the typical configuration found in the surface layer of cartilage. Twenty networks were developed, each representing one of three distinct crosslink density levels: high, medium, and low. This setup enabled us to investigate the effects of varying fibril connectivity on the network's morphology and its stress and strain responses under continuous biaxial tensile forces and cyclic loading, simulating the contact forces experienced by knee cartilage during walking. It was found that highly-crosslinked meshwork had greater stiffness than lower-crosslinked meshwork but with higher fibril strain under constant load, and that both the collagen meshwork and individual fibrils became stiffer with reduced deformation after several cycles. The current FE modeling approach provides new insights into the structure-function relationships of the collagen-like meshwork, with a specific focus on the unique role of fibril connectivity under mechanical loads. The current results suggest that collagen stiffening after several cyclic loading may lead to the embrittlement of collagen fibrils, altering the mechanical behavior of the cartilage. This study provides further evidence of the importance of the interfibrillar morphology of collagen meshwork in the mechanical behavior of cartilage. The current model illustrates the functional behavior of the collagen network and can be integrated into more comprehensive multiscale cartilage models that include additional components such as water and proteoglycans, thereby enabling a more complete representation of cartilage mechanics. Future research may utilize this collagen-centric model within broader, multi-phase frameworks to examine interactions between the collagen structure, fluids, and the proteoglycan network. These insights into fibril crosslink density-dependent mechanics may help elucidate early micro-mechanical changes occurring during osteoarthritis progression.