Issue 49

M. Hamdi et alii, Frattura ed Integrità Strutturale, 49 (2019) 321-330; DOI: 10.3221/IGF-ESIS.49.32 325 u k           and k u           (10) Respectively, where the subscripts k and u denote the known and unknown components, respectively. Eqn. (9) can be rewritten as u uk uu k k u kk ku D D D D                        (11) Rearranging Eq. (11) gives 1 1 1 1 u uk uu ku kk uu ku k k k ku kk ku D D D D D D D D D                                (12) From which the global response of SG can be fully determined. E VALUATION OF MSG - BASED MICROMECHANICS n this section, the efficiency and accuracy of MSG-based micromechanics analysis approach implemented in SwiftComp are critically evaluated. Micromechanics analysis code MAC/GMC 4.0 is chosen as a reference method during efficiency evaluation. The predictions by commercial finite element analysis code Abaqus are chosen as bench-marks during accuracy evaluation. For comparison purposes, all simulations were run on the same computer. Composites such as a continuous fiber-reinforced composite, a particle-reinforced composite, two discontinuous fiber- reinforced composites, and a woven composite are analyzed using SwiftComp, GMC, and 3D FEA. In each example, the effective properties of a composite, the computing time of each approach, and the distributions of the local stress are investigated. Meanwhile, SwiftComp along with coarse meshes, say SwiftCompR, is also used to better evaluate the efficiency of MSG. C ONTINUOUS FIBER - REINFORCED COMPOSITE irst consider a continuous fiber-reinforced composite consisting of an aluminum matrix and numerous cylindrical, boron continuous fibers arranged in a square array, with a Volume Fraction of Fibers (VOF) of 40%. Let the elastic constants of boron and aluminum values listed in Tab. 2 are taken, where E and υ denote Young’s modulus and Poisson’s ratio, respectively. Let the SG of this composite consist of a square matrix and a circular fiber located at its center (Fig. 1). Choose the center of SG as the origin of local coordinates, i y , and fiber direction length and directions of SG as xx , yy , and zz directions, respectively. Figure 1 : SG of a continuous fiber-reinforced composite. I F Square pack Microstructure zz yy