A “multicontinuum” approach to structural analyses of composites is described. A continuum field is defined to represent each constituent material along with the traditional continuum field associated with the composite. Finite element micromechanics is used to establish relationships between composite and constituent field variables. These relationships uncouple the micromechanics from structural solutions and render an efficient means of extracting constituent information during the course of a finite element structural analysis. Equations are developed for the case of a linear elastic reinforcing material embedded in a linear viscoelastic matrix and verified by comparison with results of finite element micromechanics.

1.
Aboudi, J., 1991, Mechanics of Composite Materials: A Unified Micromechanics Approach, Elsevier, Amsterdam.
2.
Brockenbrough
J. R.
,
Suresh
S.
, and
Wienecke
H. A.
,
1991
, “
Deformation of Metal Matrix Composites with Continuous Fibers: Geometrical Effects of Fiber Distribution and Shape
,”
Acta Metall. Mater.
, Vol.
39
, No.
5
, pp.
735
752
.
3.
Cook, R. D., Malkus, D. S., Plesha, M. E., 1989, Concepts and Applications of Finite Element Analysis, John Wiley and Sons, New York.
4.
Dvorak
G. J.
,
1992
, “
Transformation Field Analysis of Inelastic Composite Materials
,”
Proc. R. Soc. London
, Vol.
437
, pp.
311
327
.
5.
Dvorak
G. J.
and
Benveniste
Y.
1992
, “
On Transformation Strains and Uniform Fields in Multiphase Elastic Media
,”
Proc. R. Soc. London
, Vol.
437
, pp.
291
310
.
6.
Dvorak
G. J.
,
Bahei-El-Din
Y. A.
,
Wafa
A. M.
,
1994
, “
Implementation of the Transformation Field Analysis for Inelastic Composite Materials
,”
Comput. Mech.
, Vol.
14
, pp.
201
228
.
7.
Eshelby
J. D.
,
1957
, “
The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems
,”
Proc. R. Soc. London
, Vol.
241
, pp.
376
396
.
8.
Flu¨gge, W., 1967, Viscoelasticity, Blaisdell, Waltham, MA.
9.
Garnich
M. R.
, and
Hansen
A. C.
,
1996
, “
A Multicontinuum Theory for Thermal-Elastic Structural Analysis of Composites
,”
J. Compo. Mater.
, Vol.
31
, No.
1
, pp.
71
86
.
10.
Hashin
Z.
,
1965
, “
Viscoelastic Behavior of Heterogeneous Media
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
32
, pp.
630
636
.
11.
Hill
R.
,
1963
, “
Elastic Properties of Reinforced Solids: Some Theoretical Principles
,”
J. Mech. Phys. Solids
, Vol.
11
, pp.
357
372
.
12.
Hughes
T. J. R.
,
Taylor
R. L.
,
1978
, “
Unconditionally Stable Algorithms for Quasi-Static Elasto/Visco-Plastic Finite Element Analysis
,”
Comput. & Struct.
, Vol.
8
, pp.
169
173
.
13.
Krishnaswamy
P.
,
Tuttle
M. E.
, and
Emery
A. F.
,
1990
, “
Finite Element Modeling of Crack Tip Behavior in Viscoelastic Materials, Part I: Linear Behavior
,”
Int. J. Num. Meth. Engng.
, Vol.
30
, pp.
371
387
.
14.
Levy
A.
, and
Pifko
A. B.
,
1981
, “
On Computational Strategies for Problems Involving Plasticity and Creep
,”
Int. J. Num. Meth. Engng.
, Vol.
17
, pp.
747
771
.
15.
Mehrabadi
M. M.
, and
Cowen
S. C.
,
1990
,
Eigentensors of Linear Anisotropic Elastic Materials
,
J. Mech. Appl. Math.
, Vol.
43
, pp.
15
41
.
16.
Nemat-Nasser, S., and Hori, M., 1993, Micromechanics: Ovelzlll Properties of Heterogeneous Materials, Elsevier, Amsterdam.
17.
Pecknold
D. A.
, and
Rabman
S.
,
1994
, “
Micromechanics-Based Structural Analysis of Thick Laminated Composites
,”
Computers and Struct.
, Vol.
51
, No.
2
, pp.
163
179
.
18.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1989, Numerical Recipes, The Art of Scientific Computing (FORTRAN Version), Cambridge University Press, Cambridge, UK.
19.
Ravichandran
K. S.
, and
Seetharaman
V.
,
1993
, “
Prediction of Steady State Creep Behavior of Two Phase Composites
,”
Acta Metall. et Mater.
, Vol.
41
, No.
12
, pp.
3351
3361
.
20.
Schapery, R. A., 1974, “Viscoelastic Behavior and Analysis of Composite Materials,” Composite Materials, Vol. 2, G. P. Sendeckyj, ed., Academic Press, New York, pp. 85–168.
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