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49. Phys. 58, 2478-2486, 1985. 50. Mater. 14, 144-159, 1980. 51. Sol. 2, 58-61, 1967. 52. D 24, 1673-1686, 1991. 53. Com. 16, 563-569,1992. J. Böhm Vienna Technical University, Vienna, Austria ABSTRACT In this Chapter a Mori-Tanaka-type micromechanical method for modeling the thermoelastic behavior of composites with aligned reinforcements is described in some detail. The basic assumptions underlying mean field approaches are discussed, and a nurober of general relations between the elastic tensors, the concentration tensors and the mean fields are given.

E. the fibers are all oriented in the same direction (which hardly is met in reality), transversely isotropic behavior can be assumed and the Young's modulus in fiber direction is estimated by (46), with I E(f) E(m)- 1 fiE, = EU) I E(m) + (2lld) (47), and in transverse direction (48), with 31 Micromechanics for Macroscopic Material "'E, = E(f) I E(m) - 1 EU) I E(m) + 2 (49). Figure 9 shows the longitudinal stiffnesses of short-fiber composites as a function of fiber aspect ratio l I d. For comparison the longitudinal stiffnesses of the corresponding continuous-fiber composites with the same fiber volume fractions are also shown.

B. _ V U. B. {80). d) Spherical Particles, Generalized Self Consistent Method Christensen [37] derived effective elastic parameters by a generalized self consistent scheme. For example, the expressions for the effective bulk modulus ( ~ K =Km + {( K(p) - K(m) )3K(m) 3K(m) + 4G(m) + 4G(m) + 3(1- {)(K(p)- K(m)) ( 81 ) is exactly the same as obtained by a Mori-Tanaka approach, see below. e) Spherical Particles, Mori-Tanaka Approach Using a Mori-Tanaka type approach Benveniste [36] presents following relations: K = K(Tn) G = a

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