The goal of this project is to contribute to the development, analysis, and implementation of variational models for the mechanics of defects in solids, derived inductively from first principles, analyzed using the same mathematical methodology, and implemented on parallel supercomputers in a compatible numerical framework. Specifically, the investigator studies a concept of thermodynamically consistent evolutions as an alternative to global minimality for rate-independent material models. These evolutions are based on criticality and energy balance and avoid some of the paradoxes of global minimization while remaining compatible with first principles. The investigator also develops a novel, rigorous, and efficient numerical approach to plasticity, also based on a variational model.
The controversies around hydraulic stimulation in gas shales, induced seismicity and subsidence near geothermal fields, and sinkholes caused by collapsing made-man caverns and over-extraction of water from aquifers highlight how technology has gotten ahead of the predictive understanding of failure in solids. The goal of this project is to study consistent models for the mechanics of defects. These models for fracture, damage, and plasticity are well-rooted in theory yet applicable to realistic situations. They are implemented on parallel supercomputers in such a way that they can easily be combined in order to study complex problems. As applications, the investigator studies fracture of deep underground salt domes leading to surface sinkholes, fracture in thin films, which are commonly used in thermal barrier coatings in turbines, and damage in the manufacturing of micro-mechanical devices and sensors. The outcomes of this project affect diverse areas and industries ranging from geo-mechanics to structural engineering.
