UC San Diego

Soft materials and structures are increasingly important in biomedical systems, wearable technologies, soft robotics, and architected materials because their compliance and capacity for large deformation enable functions difficult to achieve with conventional rigid materials. Their reliable application, however, requires predicting when deformation localizes and fracture compromises structural integrity. This becomes challenging in systems involving nonlinear deformation, complex geometry, anisotropy, discrete structural organization, or time-dependent material response. This dissertation develops physically interpretable fracture-prediction frameworks based on continuum mechanics, using analytical and computational models to capture the governing relationships among loading, geometry, constitutive behavior, and fracture.The work begins by investigating whether continuum fracture mechanics can provide a useful predictive framework for a materially continuous but microstructurally complex soft system. Aortic dissection, a life-threatening condition whose defining mechanical process is tear propagation within the aortic wall, provides a direct and compelling application of fracture mechanics. By representing the wall as an effective continuum, a semi-analytical model relates loading, geometry, and constitutive behavior to the fracture-driving force. Comparisons with finite-element calculations and reported aortic fracture resistance demonstrate how the framework can identify mechanically favorable conditions for tear propagation. The dissertation then examines whether continuum fracture concepts remain applicable to periodic soft lattices. Although homogenization provides a simpler description than full-scale models that explicitly resolve individual unit cells, its connection to local rupture is not immediately evident. For elastic hexagonal lattices, the macroscopic driving force for fracture is related to the local deformation at the crack tip, enabling fracture conditions and structural trends to be identified with reduced computational effort. This continuum-to-lattice framework is subsequently extended to viscoelastic lattices, where crack evolution is time-dependent even under fixed macroscopic deformation. Rather than prescribing an independent crack-growth or traction law, a local failure criterion is combined with physically motivated assumptions and event-resolved finite-element calculations. The resulting reduced-order fracture model evaluates how viscoelasticity affects delayed failure, intervals between successive events, and overall crack-evolution trends. Together, these studies demonstrate how continuum mechanics-based fracture models can be formulated and extended as soft systems progress from effective continuous materials to discrete nonlinear structures and, finally, to time-dependent viscoelastic fracture.