SERVE-Boundary Conditions
315
Fig. 12 Variation of (a) the normalized homogenized stiffness tensor ¯
C 1111 /E M and (b) error in
¯
C 1111 , as a function of increasing SERVE size. (Reprinted from: Kubair and Ghosh [35])
Fig. 13 Convergence of homogenized stiffnesses for S 2 (r) and S 2 (r, θ)-based ESBCs with
increasing SERVE size: (a) variation of the normalized homogenized stiffness tensor ¯
C 1111 /E M
and (b) variation of the normalized error. (Reprinted from Kubair and Ghosh [35])
4.2 Comparing Convergence of ESBC-Based SERVE with
Statistical Volume Elements (SVEs)
Statistical volume elements (SVEs) are based on the ergodicity hypothesis that
the composite microstructure with dispersed heterogeneities is statistically homogeneous, and hence, its volume averages are identical to the ensemble averages
[44, 45]. In this approach, the homogenized modulus for the MVE is expected
to be equal to the mean of the volume-averaged modulus obtained from a large
315
Fig. 12 Variation of (a) the normalized homogenized stiffness tensor ¯
C 1111 /E M and (b) error in
¯
C 1111 , as a function of increasing SERVE size. (Reprinted from: Kubair and Ghosh [35])
Fig. 13 Convergence of homogenized stiffnesses for S 2 (r) and S 2 (r, θ)-based ESBCs with
increasing SERVE size: (a) variation of the normalized homogenized stiffness tensor ¯
C 1111 /E M
and (b) variation of the normalized error. (Reprinted from Kubair and Ghosh [35])
4.2 Comparing Convergence of ESBC-Based SERVE with
Statistical Volume Elements (SVEs)
Statistical volume elements (SVEs) are based on the ergodicity hypothesis that
the composite microstructure with dispersed heterogeneities is statistically homogeneous, and hence, its volume averages are identical to the ensemble averages
[44, 45]. In this approach, the homogenized modulus for the MVE is expected
to be equal to the mean of the volume-averaged modulus obtained from a large