H. Ismar, F. Streicher /Computational Materials Science 16(1999)17-24 1200=45% 1400 V=30% 100m=4 至10m=8 0.0020.40.60.81.01.21.41.61.8 0.002040.60.81.01.21.41.61.8 strain E, [%] strain e2[%] g120=45% 1=45 b800 方200 00.20406081.01.21.41.61.8 000.2040.60.81.01.21.41.61.8 strain E, [ % strain E, [% 1400 1200y=45% 1400 m=16 1001m=8 200 0.00.20.40.60.81.01.2141.61.8 02040.6081.01.21.41.61.8 strain E, [ strain E, [% Fig. 5. Variation of the fiber Weibull parameter Fig. 6. Variation of the fiber volume fraction ur [18] that for n=20 the behavior of the macro- structure in Figs. 5 and 6 on the composi structure can be assumed to be characteristic of the behavior whole structure. In Fig. 7 the build-up of the First the Weibull-shape parameter mr is varied macrostructure is shown schematically. The cal- by using a constant fiber volume fraction of culated mechanical behavior of 20 substructures is Ur=45%. The resulting nonlinear stress-strain statistically distributed to the finite elements of the relations for mf=4, 8 and 16 are shown in Fig 8. macrostructure. In this way it is possible to study The interval of strain from the beginning of fiber the influence of the fiber Weibull parameter and breaking to the balanced stress state after fracture the fiber volume fraction carried out for the sub of the last fiber becomes smaller with increasing[18] that for n ˆ 20 the behavior of the macro￾structure can be assumed to be characteristic of the whole structure. In Fig. 7 the build-up of the macrostructure is shown schematically. The cal￾culated mechanical behavior of 20 substructures is statistically distributed to the ®nite elements of the macrostructure. In this way it is possible to study the in¯uence of the ®ber Weibull parameter and the ®ber volume fraction carried out for the sub￾structure in Figs. 5 and 6 on the composite behavior. First the Weibull-shape parameter mf is varied by using a constant ®ber volume fraction of vf ˆ 45%. The resulting nonlinear stress±strain relations for mf ˆ 4; 8 and 16 are shown in Fig. 8. The interval of strain from the beginning of ®ber breaking to the balanced stress state after fracture of the last ®ber becomes smaller with increasing Fig. 6. Variation of the ®ber volume fraction vf Fig. . 5. Variation of the ®ber Weibull parameter mf . 22 H. Ismar, F. Streicher / Computational Materials Science 16 (1999) 17±24