| EPSRC Reference: |
GR/J66164/01 |
| Title: |
TWO-SIDED BOUNDS FOR THE PROPERTIES OF NONLINEAR COMPOSITES |
| Principal Investigator: |
Willis, Professor J |
| Other Investigators: |
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| Department: |
Applied Maths and Theoretical Physics |
| Organisation: |
University of Cambridge |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 September 1994 |
Ends: |
31 December 1994 |
Value (£): |
9,092
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Summary on Grant Application Form |
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The application is to fund a visit by Professor Ponte Castaeda of four months duration. The areas to be addresses will include: (1) Bounds for nonlinear creep of polycrystals. Recent work by Ponte Castaeda and deBotton, on limit analysis and on creeping materials suggests that a new bound for nonlinear polycrystals, obtained via the original procedure may give away more than necessary. In addition, it also appears that a well established self-consistent estimate may violate the associated bound. This problem will be investigated with the possible outcome of finding a better way of using the original method. (2) Two-sided bounds for composite with prescribed higher-order statistics. An attempt will be made to combine this with ideas in [12,13,14] to develop an alternative and perhaps more efficient way of obtaining the other bound, and to generalise it to permit allowance for higher-order statistics. (3) Bounds for nonlinear composites with prescribed morphological features. Essentially all the work to date on nonlinear bounds has been for random composites with prescribed point correlation functions . However, it is well known that point correlation functions neglect sometimes crucial information about the distribution of the phases, such as identification information for the matrix and inclusion phases in composites with particulate microstructures. The use of comparison linear composites will be explored in this connection, with the objectives of allowing specific morphological features. (4) Optimality of the nonlinear bounds. Recent collaboration of Ponte Casteada with P Suquet (Marseille) [20] has resulted in exact small-contrast perturbation expansions for the effective properties of certain classes of nonlinear composites. Interestingly, at least for statistically isotropic two-phase composites, these asymptotic expansions do not agree with the explicit bounds obtained so far for nonlinear composites (by any of the above-described methods). The difference is apparent in that the bounds are independent of the determinant of the stress, whereas the exact expansions (to second-order in the contrast) exhibit explicit dependence on the determinant. This difference between the bounds and the asymptotic results suggest that the bounds obtained so far may not be optimal (i.e., the best bounds possible with the given information) in general. This important issue will be investigated further with the goal of eventually generating optimal bounds, or at least estimating how far the current bounds may be from being optimal.
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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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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.cam.ac.uk |