[MAP Logo]

Materials Algorithms Project
Program Library


  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.

T.W. Clyne: twc10@cus.cam.ac.uk

Released: January 1998.
Added to MAP: October 1999.

Top | Next


This program calculates the thermal expansion coefficient (expansivity) of a composite material, using the Eshelby equivalent homogeneous inclusion method.

Top | Next | Prev


Product form:Executable files for use on almost any Apple Macintosh or PC.

Complete Program.

Top | Next | Prev


This program calculates the thermal expansion coefficient (expansivity) 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 expansivity, 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 2 different files:

<filename>.axi - axial expansivity
<filename>.tra - transverse expansivity

(<filename> refers to a user-supplied name for the output files.)

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), but even on a relatively slow machine and with the maximum number of values (100), the program only takes a few seconds to run.

Top | Next | Prev


  1. T.W. Clyne and P.J. Withers, 1993, An Introduction to Metal Matrix Composites, (Cambridge: Cambridge University Press), 120-121.

Top | Next | Prev


Input parameters

Output parameters

f - The volume fraction of the reinforcement (between 0 and 1).
alphaAx - Thermal expansivity of the composite in the axial direction (microstrain/K).
alphaTr - Thermal expansivity of the composite in the transverse direction (microstrain/K).

The following files are produced which contain the output:

<filename>.axi - reinforcement volume fraction and axial thermal expansivity
<filename>.tra - reinforcement volume fraction and transverse thermal expansivity

Top | Next | Prev

Error Indicators


Top | Next | Prev


No information supplied.

Top | Next | Prev

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.

Top | Next | Prev


1. Program text

Complete program.

2. Program data

Eshelby model for the thermal expansivity of composites
 @ CM Warwick & TW Clyne, Cambridge University, 1991
 ref: An Introduction to Metal Matrix Composites, T.W.Clyne & P.J.Withers, CUP (1993), p.120-121
(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 reinforcement Young's modulus (in GPa)  34.1
Enter reinforcement Poisson ratio  0.31
Enter matrix thermal expansivity (in microstrain/K)  10
Enter reinforcement thermal expansivity (in microstrain/K)   79
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

Computation complete.  Output is stored in 2 files.
Enter prefix for these data files eshcte

3. Program results

Below are the output files:


              f  alphaAx(Ástrain/K)
 0.00000000000E+0000 1.00000000000E+0001
 2.00000000000E-0002 1.03620792072E+0001
 4.00000000000E-0002 1.07351764481E+0001
 6.00000000000E-0002 1.11198038743E+0001
 8.00000000000E-0002 1.15165059495E+0001
 1.00000000000E-0001 1.19258620422E+0001
 1.20000000000E-0001 1.23484892735E+0001


              f  alphaTr(Ástrain/K)
 0.00000000000E+0000 1.00000000000E+0001
 2.00000000000E-0002 1.07109017430E+0001
 4.00000000000E-0002 1.14369027116E+0001
 6.00000000000E-0002 1.21784757574E+0001
 8.00000000000E-0002 1.29361127654E+0001
 1.00000000000E-0001 1.37103255381E+0001
 1.20000000000E-0001 1.45016467210E+0001

Top | Next | Prev

Auxiliary Routines


Top | Next | Prev


composite, laminate, coating, thermal, expansion, expansivity, reinforcement, matrix, Eshelby

Top | Next | Prev


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

Top | Prev

MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

MAP Website administration / map@msm.cam.ac.uk

Top | Index | MAP Homepage Valid HTML 3.2!