Finite Element and Finite Difference Programs for Computing the Linear
Electric and Elastic Properties of Digital Images of Random Materials, 1998
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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.