Variational phase-field models of fracture

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This research proposal deals with phase-field models of fracture. This approach, which I created with G. Francfort and J.-J. Marigo, is based on the minimization of a diffused interface approximation of a fracture energy recasting Griffith's classical theory as an energy minimization principle. It addresses some of the biggest challenges in fracture mechanics: path identification, crack nucleation, and change of morphology. The long term objective of my research program is the rigorous construction of models applicable to a variety of problems involving fracture, their mathematical analysis and numerical implementation, and their diffusion towards a broad public in academia and industry. The proposed research program is articulated around three specific short-term objectives (ST1-3). (ST1) is the development, analysis and numerical implementation of adjoint-based second order solvers. (ST2) deals with the extension of the parareal time-parallelization technique to variational phase-field fracture (and other rate-independent processes), and its implementation. (ST3) is concerned with the mathematical analysis and implementation of the driving force approach to nucleation, and the derivation of a dual-criterion model accounting for strength (a stress-based nucleation criterion) and toughness (propagation following Griffith's criterion). The specific objectives developed in this proposal have been identified as major roadblock towards the predictive understanding of fracture in discussion sessions held during conference mini-symposia or research workshops. This research program will lead to groundbreaking advances on the predictive understanding and numerical simulation of fracture. It will have a direct impact on many fields including: the fracture of hard and soft biological tissues; fracture of composite materials, essential to the aerospace and automobile industry; manufacturing techniques such as laser cutting of glass and electromagnetic cutting of metals; mitigating the societal impact of climate change through the predictive understanding of fracture of ice sheets or the design of fractured reservoir for carbon sequestration; and materials science including the design of micro-structured materials with extreme fracture properties. These research activities share two additional aspects: All products will be implemented in the open-source software code vDef which I maintain and is used in multiple industry and academic research departments by experts and non-experts. HQP will be involved in the creation of documentation, validation tests and tutorials for each component. HQP will be trained in a vertically integrated, multi-disciplinary environment. They will participate in multi-disciplinary and multi-institutions group meetings and discussions connected with my other ongoing research projects on the field of fracture mechanics.