The constitutive framework documented in served as the basis for various structural models in the context of fiber-reinforced composites. By accounting for the microstructure, it also formed the foundation for the mechanical analysis of a wide range of soft biological tissues--including arteries in both healthy and pathological states, myocardium, heart valves, corneas, lens capsules, ligaments, skin, cartilage, temporomandibular joint discs, and intervertebral discs, to name but a few. This constitutive framework is also employed to describe the mechanical behavior of engineered materials, such as textile composites, as well as anisotropic hyperelastic solids in general. Given that collagen fiber orientation in many soft biological tissues exhibits a certain degree of dispersion, we have extended our model to include two additional scalar structural parameters that characterize the asymmetric distribution of collagen fiber orientation.

This lecture summarizes the development of a structural model and focuses on the challenges associated with modeling soft biological tissues--such as arterial walls and the myocardium--in health and disease, e.g., in cases of aortic dissection. In particular, a patient-specific computational model of aortic dissection is presented that accounts for fluid-structure interaction and enables a better understanding of system behavior in response to specific parameter changes.