This project deals with fundamental theoretical development, computational methods synthesis, and experimental calibration/validation in the area of fracture of ductile metallic structural elements. Whereas sophisticated constitutive response, large deformations, and intricate geometry are presently handled as a matter of routine, existing capabilities in the realm of fracture are still very much confined to symmetric, highly idealized scenarios and simple material response. The aim of this project is to move mechanics-based simulation of fracture processes closer to the level of sophistication enjoyed by deformation processes. With respect to theoretical modeling of fracture processes, the core innovative concept relates to a novel regularization of the continuum problem, which contrasts in important ways with the prevailing cohesive zone- type approach. In this theory, fracture phenomenology has a natural expression: a separation function delineates the limiting conditions in the bulk continuum that lead to fracture. The concept is analogous to the yield function in elasto-plasticity. Other innovations relate to the computational realization of the fracture theory. Chief among these is the variable-element-topology finite element method, which is a general finite-element-type Galerkin method that embraces general polyhedral elements, thereby vastly simplifying automatic adaptive meshing. Another key innovation relates to remapping of the material state from one mesh realization to the next - a necessary operation whenever evolutionary mesh redesign is required. An extensive program of experimentation will be an integral part of the proposed project.
The project will support two graduate-student researchers, one at the MS level and one at the PhD level. Other educational and outreach activities are also planned. A notable element of the project is the planned approach to software design, development, testing, dissemination, and collaboration. This strategy places an emphasis on efficiency, in human-effort terms, of technology sharing and transfer. This approach is driven by the perception that rapid forward progress in Simulation-Based Engineering Science is possible, but will require a new model for software synthesis in the academic community.
