Hybrid Local/Nonlocal Continuum Mechanics Modeling and Simulation for Material Failure

The classical continuum mechanics, which studies the mechanical behavior of structures based on partial differential equations, shows its deficiencies when it encounters a discontinuity. Peridynamics based on integral equations can simulate fracture but suffers from high computational costs. A hybrid local/nonlocal model combining the advantages of peridynamics with those of classical continuum mechanics can simulate fracture and reduce the computational cost. Under the framework of the hybrid local/nonlocal model, this research developed an approach and computational codes for fracture simulations. First, we developed the computational codes based on the hybrid model with a priori partition of the domain between local and nonlocal models to tackle engineering problems with relevant level of difficulty. Second, we developed a strength-induced approach to enhance the capability of the computational codes because the strength-induced approach can limit the peridynamic model to necessary computational steps at the time level and a relatively small zone at the space level during a simulation. The strength-induced approach also improved the hybrid models by enabling an automatic partition of the domain without manual involvement. At last, a strength-induced computational code was developed based on this research. This dissertation complemented and illustrated numerically some previous work of Cohmas laboratory, in which a new route was introduced toward simulating the whole process of material behaviors including elastic deformation, crack nucleation and propagation until structural failure.