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- National Science Foundation, Division of Mathematical ScienceVariational approaches to defect mechanics
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.
Amount: $163886National Science Foundation, DMREF programDesigning Microstructures for Engineering Toughness
This collaborative project with with K. Bhattacharya, K. Faber and G. Ravichandran, (Caltech) brings together an interdisciplinary team with the vision of exploiting digital manufacturing methods, including 3D printing and ink-jet printing, to synthesize structural materials with exceptional mechanical properties. It has long been understood that the fine-scale structure of materials -- the microstructure -- can affect mechanical properties, and this has been exploited in both materials processing and in creating composite materials. However, such effort has historically been limited in the range of microstructures that could be explored. The vision here is to overcome this limitation by adapting methods of digital and additive manufacturing -- which emerged and have largely been used as tools for prototyping -- to make structural materials with superior mechanical performance. The investigators specifically focus on fracture because of its existential engineering importance and because it raises deep scientific questions. This project will provide for the training through research involvement of doctoral students as well as undergraduate researchers in an interdisciplinary setting, and a new opportunity for engaging K-12 students and for promoting STEM education amongst underrepresented groups. Fracture is a free discontinuity problem, and homogenization and optimal design of such problems is a long-standing intellectual challenge. In this project, new theoretical and computational approaches addressing this challenge will be pursued. The free boundary problem will be regularized using a variational fracture field approach, and crack propagation will be studied subject to a new surfing boundary condition. Optimal design of the microstructure will be pursued through parametric optimization and topology optimization applied to trajectories. Innovative approaches will be explored to adapt prototyping methods to the synthesis of structural materials with designed microstructures. While 3D printing and related methods for plastics have gained considerable attention, these strategies will be pursued here to synthesize structural ceramics at the appropriate size scales. Finally, emerging experimental methods, including digital image correlation, X-ray computed tomography, and confocal microscopy, will be employed to provide both insight into and validation of the theoretical studies of the complex process of fracture in heterogeneous materials.
A. A. Leòn-Baldelli and B. Bourdin (2015) On the asymptotic derivation of Winkler-type energies from 3D elasticity In: Journal of Elasticity
A. Mesgarnejad, B. Bourdin, and M. Khonsari (2015) Validation simulations for the variational approach to fracture In: Comput. Methods. Appl. Mech. Engng
M. Z. Hossain, C-J Hsueh, B. Bourdin, and K. Bhattacharya (2014) Effective toughness of heterogeneous media In: J. Mech. Phys. Solidshttp://dx.doi.org/10.1016/j.jmps.2014.06...
A. A. Lèon-Baldelli, J.-F. Babadjian, B. Bourdin, D. Henao, and C. Maurini (2014) A variational model for fracture and delamination of thin films In: J. Mech. Phys. Solidshttp://dx.doi.org/10.1016/j.jmps.2014.05...
B. Bourdin, J.-J. Marigo, C. Maurini, and P. Sicsic (2014) Morphogenesis and propagation of complex cracks induced by thermal shocks In: Phys. Rev. Lettershttp://dx.doi.org/10.1103/PhysRevLett.11...