Diffusion-Driven Fracture

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Fracture mechanics is often concerned with predicting the development and propagation of cracks in materials subject to given forces. In some situations, however, the actual forces depend strongly on the geometry of the cracks themselves. A classical example is that of mud-crack patterns induced by evaporation, which is itself strongly influenced by the development of new crack surfaces. Other problems of this class are commonly encountered in hydraulic fracturing, fracture in ferro- and piezoelectric materials, corrosion stress fracture of metals, environmental stress fracture of glass and polymers, fracture of electrodes in lithium-ion batteries, thermal cracks, and ion diffusion in cements. In this project, the investigator constructs rigorous models for such diffusion-driven fracture problems, develops computer codes for the models on parallel supercomputers, and uses the models and codes to study specific problems of interest in industrial, engineering, and scientific applications. Graduate students participate in the work of the project.Variational phase-field models of fracture, originally devised by the investigator and further developed in the applied mathematics community, have seen an explosive growth in the last few years. Their main strength is their ability to address two of the most critical issues in the quasi-static fracture of brittle materials: crack path identification and crack nucleation. While mathematicians are typically concerned to find the equilibrium displacement and crack configuration of a solid under a given load, in many situations the loadings must be derived from a secondary problem and may be affected by the fracture geometry. These include hydraulic fracturing, fracture in ferro- and piezoelectric materials, corrosion stress fracture of metals, environmental stress fracture of glass and polymers, fracture of electrodes in lithium-ion batteries, thermal cracks, and ion diffusion in cements, which have been studied in a largely ad hoc manner. The goal of this project is to establish a strong theoretical foundation for phase-field models where the fracture is driven by a diffusive process. The investigator and his students implement these models and release them as open source software. They use these mathematical and computational tools to study three-dimensional crack nucleation under diffuse loads in two and three dimensions. Graduate students participate in the work of the project.