Issue 49

M. Hamdi et alii, Frattura ed Integrità Strutturale, 49 (2019) 321-330; DOI: 10.3221/IGF-ESIS.49.32 326 E (GPa) ν Boron 379.30 0.10 Aluminum 68.30 0.30 Table 2 : Elastic constants of Boron and Aluminum. In SwiftComp, the 2D SG is meshed with 8-node quadrilateral elements having 3 Degrees of Freedom (DOFs) at each node, and the meshed SG consists of 4500 elements. In SwiftCompR, number of elements is reduced to 320. HFGMC is used only in this example because HFGMC in MAC/GMC 4.0 cannot handle 3D microstructures. In GMC and HFGMC, the 2D SG is meshed with a 66×66 subcell grid. In 3D FEA, the 3D SG is needed for complete homogenization, and it is obtained by extruding the 2D SG along the fiber direction. The 3D SG is meshed with 20-node elements (SOLID95), and the meshed SG consists of 384 elements. Tab. 3 lists predicted effective properties of composite. For E1 and E2, all predictions are in perfect agreement, except that GMC slightly underestimates E2 by 2.02%. For G12 and G23, all predictions are in good agreement, except that GMC slightly underestimates G12 and G23 by 6.27% and 4.70%, respectively, and that HFGMC slightly overestimates G23 by 2.10%. Note that, although having a coarse mesh, SwiftCompR still provides perfect predictions. Tab. 4 lists the computing times. SwiftCompR ran for 0.206 second and is the fastest; GMC and SwiftComp ran for 1.34 seconds and 1.70 seconds, respectively, and are also very fast; 3D FEA ran for 1.79 seconds because it requires a 3D SG; HFGMC ran for 445 seconds, indicating it sacrifices efficiency for accuracy. In summary, when homogenizing the composite, SwiftComp and SwiftCompR are accurate and efficient, and GMC and HFGMC exhibit accuracy-efficiency tradeoffs. At last, numerical experiments indicate that, given the same meshed 3D SG, SwiftComp is as accurate, but much more efficient than 3D FEA. E 1 (GPa) E 2 (GPa) G 12 (GPa) G 23 (GPa) v 12 v 23 SwiftComp 193.53 127.68 48.30 41.70 0.2090 0.2777 3D FEA 193.53 127.68 48.30 41.70 0.2090 0.2777 GMC 193.30 125.10 45.27 39.74 0.2119 0.2809 HFGMC 193.50 127.50 48.32 42.58 0.2090 0.2789 SwiftCompR 193.53 127.68 48.30 41.71 0.2090 0.2778 Table 3 : Predicted effective properties of a continuous fiber-reinforced composite. SwiftComp 3D FEA GMC HFGMC SwiftCompR No. of elements 384 384 4356 4356 320 Time (s) 1.70 1.79 1.34 445 0.206 Table 4 : Computing time for a continuous fiber-reinforced composite. Next let composite undergo uniaxial extension in the yy direction, with 22  =0.1%. The global response of the SG can be fully determined from Eq. (12), and local fields can be subsequently recovered. Fig. 2 shows the predicted distributions of 11  along the yy axis, by different approaches. All predictions are in good agreement, except that the prediction by GMC is underestimated in the matrix. Fig. 3 shows the predicted distributions of 22  along the zz axis. The predictions by SwiftComp, SwiftCompR, and 3D FEA are in perfect agreement; the prediction by GMC noticeably deviates from the benchmark in the fiber; the prediction by HFGMC deviates from the benchmark near the fiber/matrix interface. Fig. 4 shows the predicted distributions of 33  along the yy axis. The predictions by SwiftComp, SwiftCompR, and 3D FEA are in excellent agreement; the prediction by GMC is even throughout the SG, indicating that GMC cannot effectively predict the distributions of the out-of-plane stresses with a 2D SG; the prediction by HFGMC is accurate near the center of the