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Program MAP_COMP_ESHELC

  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of subroutine's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary subroutines required.
  12. Keywords.
  13. Download source code.
  14. Links.

Provenance of Source Code

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.

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Purpose

This program calculates the elastic constants of a composite material, using the Eshelby equivalent homogeneous inclusion method.

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Specification

Language:N/A
Product form:Executable files for use on almost any Apple Macintosh or PC.

Complete Program.

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Description

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>.eax - axial Young's modulus
<filename>.etr - transverse Young's modulus
<filename>.gat - axial - transverse shear modulus
<filename>.gtt - transverse - transverse shear modulus
<filename>.nat - axial - transverse Poisson ratio
<filename>.nta - transverse - axial Poisson ratio
<filename>.ntt - transverse - transverse Poisson ratio

(<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,


nuax tr * Etr = nutr ax * Eax

and
Etr = 2 * Gtr tr * (1 + nutr tr).

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 http://www.aladdinsys.com/expander/
WINZIP at http://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.

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References

  1. T.W. Clyne and P.J. Withers, 1993, An Introduction to Metal Matrix Composites, (Cambridge: Cambridge University Press), 62-63.

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Parameters

Input parameters

Output parameters

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:

<filename>.eax - reinforcement volume fraction and axial Young's modulus
<filename>.etr - reinforcement volume fraction and transverse Young's modulus
<filename>.gat - reinforcement volume fraction and axial - transverse shear modulus
<filename>.gtt - reinforcement volume fraction and transverse - transverse shear modulus
<filename>.nat - reinforcement volume fraction and axial - transverse Poisson ratio
<filename>.nta - reinforcement volume fraction and transverse - axial Poisson ratio
<filename>.ntt - reinforcement volume fraction and transverse - transverse Poisson ratio

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Error Indicators

None.

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Accuracy

No information supplied.

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Further Comments

Further information about this program can be obtained from the Composites and Coating Group website at http://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.

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Example

1. Program text

Complete program.

2. Program data

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

3. Program results

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  

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Auxiliary Routines

None.

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Keywords

composite, laminate, coating, elastic constant, elastic, reinforcement, matrix, Young, modulus, Poisson, shear, stress, strain, Eshelby

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Download

Download MAP files
Download executable file for the PC
Download executable file for the Macintosh

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