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C.M. Warwick and T.W. Clyne,
Composites and Coatings Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.
E-mail
T.W. Clyne: twc10@cus.cam.ac.uk
Released: January 1998.
Added to MAP: October 1999.
This program calculates the elastic constants of a composite material, using the Eshelby equivalent homogeneous inclusion method.
| Language: | N/A |
| Product form: | Executable files for use on almost any Apple Macintosh or PC. |
Complete Program.
This program calculates the elastic constants of a composite material, using the Eshelby equivalent homogeneous inclusion method [1]. The composite is modelled in terms of ellipsoidal reinforcements, all with their major axis parallel to one another (the axial direction), embedded in a homogeneous matrix material. The reinforcements are assumed to be transversely isotropic and so, consequently, is the composite.
The input data required are the Young's modulus and Poisson ratio for the matrix and reinforcement, the volume fraction of the reinforcement and its aspect ratio. These are screen input in response to a series of prompts. The aspect ratio can be greater than 1 (prolate spheroids), equal to 1 (spheres) or less than 1 (oblate spheroids).
The results, as a function of reinforcement volume fraction, are written to 7 different files:
(<filename> refers to a user-supplied name for the output files.)
Note that, since the composite is transversely isotropic, its elastic properties are fully described by 5 elastic constants. There are therefore inter-relationships between the 7 calculated elastic constants. For example,
Downloading and running the program
Compiled versions of the programs have been produced as stand-alone applications. They are run simply by double-clicking on the icon concerned. They should run on virtually any Apple Macintosh or PC. Data input is via the screen. Data output is to files which are named by the user. These are produced as files for the plotting application "Kaleidagraph", but they can be read as text files from many other plotting or spreadsheet applications. These output files are normally created within the currently-active folder. The program quits after each complete set of computations. For further use, it is necessary to double-click on the icon again.
The executable files for downloading have been compressed using STUFFIT EXPANDER on the Macintosh and WINZIP or PKUNZIP on the PC. These decoders can be downloaded from the following websites:
STUFFIT EXPANDER at https://www.aladdinsys.com/expander/
WINZIP at https://www.winzip.com/
The run time depends on the number of values requested (and on machine speed). On a relatively slow machine and with a large number of values, the program may take up to a minute to run.
| Eshelby S tensor | - | dimensionless. For further details see reference 1. |
| f | - | The volume fraction of the reinforcement (between 0 and 1). |
| Eax | - | Young's modulus of the composite in the axial direction (GPa). |
| Etr | - | Young's modulus of the composite in the transverse direction (GPa). |
| Gaxtr | - | The axial - transverse shear modulus of the composite (GPa). |
| Gtrtr | - | The transverse - transverse shear modulus of the composite (GPa). |
| nuaxt | - | The axial - transverse Poisson ratio of the composite. |
| nutrax | - | The transverse - axial Poisson ratio of the composite. |
| nutrtr | - | The transverse - transverse Poisson ratio of the composite. |
The following files are produced which contain the output:
None.
No information supplied.
Further information about this program can be obtained from the Composites and Coating Group website at https://www.msm.cam.ac.uk /mmc/mmc.html and is one of a series of programs produced by Bill Clyne and co-workers in the Materials Science Department at Cambridge.
It should be noted:
Nothing is expected of anyone downloading a program and there is no obligation to use results obtained from it in any particular manner. Equally, there is no liability on the part of the supplier and no guarantee that the programs do not incorporate errors or invalid data. In general, however, the offer is aimed at researchers and is designed to stimulate collaborative work. Anyone downloading a program is therefore invited to give their address to the supplier and is also welcome to enter into contact if they wish to explore any details. In the event that results obtained using any of the programs are published in any form, it would be appreciated if their source could be acknowledged.
Complete program.
Eshelby model for the elastic constants of composites @ CM Warwick & TW Clyne, Cambridge University, 1992 ref: An Introduction to Metal Matrix Composites, T.W.Clyne & P.J.Withers, CUP (1993), p.60-62 (Unlimited distribution version - please acknowledge when publishing) Particulate or unidirectionally aligned fibre composites Mean field adaptation of the Eshelby model Enter matrix Young's modulus (in GPa) 167 Enter matrix Poisson ratio 0.31 Enter fibre Young's modulus (in GPa) 34.1 Enter fibre Poisson ratio 0.31 Enter reinforcement aspect ratio (>0) 2.5 Enter max. reinforcement volume fraction (>0 and <1) 0.12 Enter number of reinforcement volume fraction values (max. 100) 6 Calculating...... Computation complete. Output is stored in 7 files. Enter prefix for these data files eshelc
Eshelby S-tensor values:
0.6317779 0.0518272 0.1373791 0.0000000 0.0000000 0.0000000
0.0518272 0.6317779 0.1373791 0.0000000 0.0000000 0.0000000
0.0038183 0.0038183 0.2489455 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.4537740 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.4537740 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.5799507
Below are the output files:
eshelc.eax eshelc.stn
f Eax(GPa) f Etr(GPa)
0.0000000000 167.00000000 0.0000000000 167.00000000
0.0200000000 163.70907625 0.0200000000 162.08620458
0.0400000000 160.44998441 0.0400000000 157.34105941
0.0600000000 157.22226481 0.0600000000 152.75600138
0.0800000000 154.02546659 0.0800000000 148.32303594
0.1000000000 150.85914748 0.1000000000 144.03469065
0.1200000000 147.72287362 0.1200000000 139.88397311
eshelc.gat eshelc.gtt
f Gaxtr(GPa) f Gtrtr(GPa)
0.0000000000 63.74045802 0.0000000000 63.74045802
0.0200000000 62.17027442 0.0200000000 61.88816290
0.0400000000 60.63480666 0.0400000000 60.09726772
0.0600000000 59.13291599 0.0600000000 58.36476932
0.0800000000 57.66351295 0.0800000000 56.68785726
0.1000000000 56.22555471 0.1000000000 55.06389858
0.1200000000 54.81804257 0.1200000000 53.49042404
eshelc.nat eshelc.nta
f nuaxtr f nutrax
0.0000000000 0.31000000 0.0000000000 0.31000000
0.0200000000 0.30993495 0.0200000000 0.30686252
0.0400000000 0.30987175 0.0400000000 0.30386759
0.0600000000 0.30981041 0.0600000000 0.30100953
0.0800000000 0.30975094 0.0800000000 0.29828314
0.1000000000 0.30969337 0.1000000000 0.29568368
0.1200000000 0.30963770 0.1200000000 0.29320681
eshelc.ntt
f nutrtr
0.0000000000 0.31000000
0.0200000000 0.30950894
0.0400000000 0.30905335
0.0600000000 0.30863193
0.0800000000 0.30824345
0.1000000000 0.30788679
0.1200000000 0.30756089
None.
composite, laminate, coating, elastic constant, elastic, reinforcement, matrix, Young, modulus, Poisson, shear, stress, strain, Eshelby
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