| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | September 17, 2013 |
| Latest Amendment Date: | September 17, 2013 |
| Award Number: | 1312739 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Michael Steuerwalt
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 15, 2013 |
| End Date: | August 31, 2017 (Estimated) |
| Total Intended Award Amount: | $163,886.00 |
| Total Awarded Amount to Date: | $163,886.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
202 HIMES HALL BATON ROUGE LA US 70803-0001 (225)578-2760 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
Baton Rouge LA US 70803-2701 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | APPLIED MATHEMATICS |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
Bourdin
1312739
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.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
The main focus of this project has been on devising coupled phase-field models coupling damage and plasticity.
In a first stage, we developed a novel algorithm for perfect associated plasticity tha leverage recent mathematical progres on variational formulations in plasticity. Our approach is based on alternating minimization with respect to displacement and plastic strain. We then propose a dual formulation for minimization with rtespect to the plastic strain that makes implementing complex plasticity model easy, efficient and robust.
We later coupled these models with the PI's prior work on variational phase-field models of fracture. We extended the analysis of one-dimensional version of the model, and described the range of behavior based on a relative scaling of plastic and damage yield surfaces. In two and three dimension, we obtained good qualitative match of the brittle to ductile transition in Ti alloys as a function of their composition, and of necking and crack nucleation in uni-axially loaded metal rods.
This project supported the research of five undergraduate students, has been acknowledged in over 20 oral conference presentations or seminars and 6 research articles.
The codes produced as part of this project have been made available under an open source licence and are being used in the industry.
Last Modified: 01/16/2018
Modified by: Blaise A Bourdin
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