Abstract
Risk assessment in may areas of civil, mechanical, and aerospace engineering requires statistical analysis of crack formation and propagation in materials, which in turn relies on complex and computationally expensive models. Fast surrogate models are needed to alleviate the computational burden; however, the discontinuous nature of fracture dynamics presents a major challenge to most approximation methods. We introduce an approach based on reduced basis and sparse grids induced by piece-wise constant functions, which does not require assumptions on the regularity of the model response in either parameter or real space. Using a sequence of random samples (i.e., solutions to the full model), we construct a small set of basis functions that capture the variability of the displacement field for different values of the model parameters. We expand the displacement field as a linear combination of these basis functions and construct an approximation to the expansion coefficients using an ℓ2 projection onto an adaptive sparse grid basis induced by piece-wise constant functions. We demonstrate the viability of our approach with an application to a peridynamics model of crack branching in brittle soda lime glass.
Original language | English |
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Title of host publication | 19th AIAA Non-Deterministic Approaches Conference, 2017 |
Publisher | American Institute of Aeronautics and Astronautics Inc, AIAA |
ISBN (Print) | 9781624104527 |
State | Published - 2017 |
Event | 19th AIAA Non-Deterministic Approaches Conference, 2017 - Grapevine, United States Duration: Jan 9 2017 → Jan 13 2017 |
Publication series
Name | 19th AIAA Non-Deterministic Approaches Conference, 2017 |
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Conference
Conference | 19th AIAA Non-Deterministic Approaches Conference, 2017 |
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Country/Territory | United States |
City | Grapevine |
Period | 01/9/17 → 01/13/17 |
Funding
his material is based upon work supported in part by the U.S. Defense Advanced Research Projects Agency, Defense Sciences Office under contract and award numbers HR0011619523 and 1868-A017-15; by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under contract and award numbers ERKJ259; and by the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory, which is operated by UT- Battelle, LLC., for the U.S. Department of Energy under Contract DE-AC05-00OR22725.