Issue 49

M. Hamdi et alii, Frattura ed Integrità Strutturale, 49 (2019) 321-330; DOI: 10.3221/IGF-ESIS.49.32 322 3. Assign the effective properties to the macroscopic structure to determine the global response; Substitute the global response into the UC and re- cover the local (displacement, strain, and stress) fields, or to say, dehomogenize the composite. Various micromechanics approaches have been developed to predict the effective properties. The Voigt-Reuss hypothesis leads to the earliest rules-of-mixtures approaches. Hill [2] demonstrated that the Voigt-Reuss hypothesis could provide rigorous upper and lower bounds of the effective properties of a composite. However, for a real composite, the difference between these two bounds is often too big to be used in practice. There are two major strategies of overcoming this drawback, i.e., either reducing this difference or obtaining some approximations between the lower and the upper bounds. Other micromechanics approaches include the Mean Field Homogenization (MFH) [3], Hashin and Shtrik-man’s variational approach [4], the third-order bounds [5], the recursive cell method [6], and the Mathematical Homogenization Theories (MHT) [7,8]. Hollister and Kikuchi [9] evaluated the predictive capabilities of these approaches and found that, for periodic or even locally periodic composites, MHT outperformed the others. Elaborated efforts have been made not only to homogenize but also to dehomogenize composites. Aboudi [10] developed the Method of Cells (MOC) and later the Generalized Method of Cells (GMC) to achieve this goal. The GMC involves subdividing UC into numerous cuboid subcells and approximating the local quantities with their averages over each subcell. A detailed review on MOC and GMC can be found in Aboudi [11]. GMC endows a user with the capability of modelling continuous, discontinuous, woven, and smart (piezo-electomagnetic) composites. It also provides libraries of nonlinear deformation, damage, failure, and fiber/matrix debonding models, continuous and discontinuous repeating UCs, and material properties. The software suite is available from NASA Glenn [12,13]. Despite advantages, GMC suffers from two major drawbacks. First, meshing UC with a subcell grid introduces considerable domain approximation errors. Note that it is more accurate to mesh UC with a finite element mesh. Second, approximating the local quantities with averaged values introduces considerable approximation error. Note that it is more accurate to reproduce the local quantities with shape functions and nodal values. Aboudi [11] developed the High Fidelity Generalized Method of Cells (HFGMC) to incorporate some mechanisms ignored by GMC (e.g., axial shear coupling). Williams, et al. [14] demonstrated that HFGMC was more accurate yet more computationally costly than GMC. Recently Yu [15] proposed the Mechanics of Structure Genome (MSG), which is concerned with the constitutive modelling for composites, based on the concept of Structure Genome (SG). Generalized from the concept of RVE, SG is defined as the smallest mathematical building block of a structure. The MSG is an unified approach to constructing the constitutive models for structures such as 3D structures, beams, plates, and shells, over multiple length scales. One of its unique features is that it bridges the micromechanics analysis of a microstructure with the structural analysis of a corresponding macroscopic structure. The MSG has been implemented in SwiftComp TM , a general-purpose commercial code for multiscale constitutive modelling. SwiftComp can homogenize and dehomogenize a wide variety of periodic, partially periodic, and aperiodic composite structures such as composite laminates, woven composites, sandwich panels, corrugated plates, and many other build-up structures. The objective of this paper is to critically evaluate the accuracy and efficiency of the general-purpose micromechanics approach based on MSG, when it is applied to 3D structures. GMC is chosen as a reference method for efficiency evaluation. The predictions by 3D FEA are chosen as benchmarks during accuracy evaluation. Composites such as a continuous fiber-rein- forced composite, a particle-reinforced composite, two discontinuous fiber-reinforced composites, and a woven composite are analyzed using MSG, GMC, and 3D FEA. M SG - BASED MICROMECHANICS SG provides a general-purpose micromechanics theory when it is applied to the constitutive modeling of 3D structures. The term of “genome” means that SG contains all the constitutive information needed to define a structure in the same fashion as a genome containing all the intrinsic information for an organism’s growth and development. Although SG seems to play a role similar to RVE, they are essentially distinct, even for the structural analysis of 3D bodies. This can be understood by looking into structures made of composites having 1D, 2D, and 3D heterogeneities (Tab. 1). For a 1D heterogeneity (e.g., a binary composite consisting of two alternating phases), SG is a line segment consisting of the connecting subline segments with each subline segment representing each phase; for 2D heterogeneity (e.g., unidirectional fiber-reinforced composite), SG is 2D domain; for 3D heterogeneity, SG is 3D. Clearly, to describe heterogeneity, SG can have a dimension as low as that for heterogeneity, while RVE must have a dimension determined not only by heterogeneity but also by the type of properties required by structural analysis. M