| EPSRC Reference: |
GR/S99044/01 |
| Title: |
Mathematical Analysis of the Static and Dynamic Behaviour of Materials with Phase Transistions and Microstructures |
| Principal Investigator: |
Zimmer, Professor J |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematical Sciences |
| Organisation: |
University of Bath |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
18 March 2005 |
Ends: |
17 March 2008 |
Value (£): |
69,172
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Continuum Mechanics |
| Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The proposed research topic is the mathematical analysis of materials with microstructures, in particular, the investigation of the static and dynamic behaviour on the crystalline level and consequences on the continuum scale.Mathematical progress over the last few years has focused on the static situation, based on variational principles. The major challenge is now to understand the dynamics of such materials. Specifically, the investigation of critical points (rather than global minima of the energetic landscape as given by variational principles) is important to describe the behaviour of many materials. In particular, we propose to study the evolution of Young measures by means of a gradient flow. A suitable mathematical framework is to be developed and applied to damage, plasticity, and possibly fracture.Additionally, a framework for the derivation of physically relevant energies with a large number of parameters will be established, which is pending due to the wealth of newly available data.Finally, the relaxation of multiphase energies and complicated energetic landscapes will be studied. Given the connection with the notion of quasiconvexity, which is central in the calculus of variations, this is an important mathematical topic in its own right. However, it is also highly relevant for applications in engineering. Certain envelopes of a nonconvex microscopic energy function of a material serve as a model for its macroscopic energy, describing the effective properties of the material. If one succeeds in determining this hull for a given microscopic energy, most computations can be carried out on the macroscopic, rather than the microscopic scale. As a result, the speed of computations can be significantly improved.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.bath.ac.uk |