Finite Element and Finite Difference Programs for Computing the Linear Electric and Elastic Properties of Digital Images of Random Materials, 1998 Go back to Part II Chapter 2 Go back to Table of Contents

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NISTIR 6269

Finite Element and Finite Difference Programs for Computing the Linear Electric and Elastic Properties of Digital Images of Random Materials

Edward J. Garboczi
Building and Fire Research Laboratory
National Institute of Standards and Technology

   
   
   
   

Cover picture: Showing, for a horizontal applied field, the horizontal currents around a circular inclusion of conductivity 10, embedded in a matrix of conductivity one, computed using a finite difference program. The magnitude of the currents go from red = high to black = low.

   
   
   
   
   

ABSTRACT

This manual has been prepared to show some of the theory behind, and the practical details for using, various finite element and finite difference computer programs that have been developed for computing the effective linear properties of random materials whose microstructure has been stored in a 2-D or 3-D digital image. Thirteen different computer programs are described, including finite element conductivity and elastic programs, finite difference programs for D.C. and A.C. conductivity, finite element elastic programs that include thermal strains (eigenstrains), and three auxiliary programs for Gaussian quadrature and phase percolation. All the programs are written in FORTRAN 77, and operate on an arbitrary digital image that is read from a file. Arbitrary symmetric conductivity tensors and arbitrary elastic moduli tensors can be used in the finite element programs. In the finite difference programs, the conductivity tensors must be diagonal. Only linear elastic and linear electrical conductivity problems are considered. The programs can of course be extended to other problems that have a similar mathematical basis.