A strain-compatible method for micromechanical analysis of multi-phase composites

Mechanics of Anisotropic Composite Materials

“…In fact at the microlevel of heterogeneous composite both stress and strain continuity hold such that the Voigt and the Reuss approximations can serve as upper and lower estimates for the effective stiffness matrix elements of anisotropic composite systems (cf. Herakovich [11], Gan et al [9]). In the impressive monograph "Micromechanics of composite materials," Aboudi et al [1] analyze the effective engineering constants of the Glass/Epoxy fibrous composite E 11 , E 22 = E 33 , ν 12 = ν 13 , ν 23 , G 12 = G 13 , G 23 as functions of fiber volume fraction V f .…”

“…Simultaneously, they have to be sufficiently small but repeatedly noticeable to assure that the representation of a uniform deformation field described by the displacement u and the gradient ∇u such that the averaged (effective) strain ε = 1 2 (∇ T u + ∇u) is justified (cf. Gan et al [9]). Note that component material at the microlevel (or nanolevel) is usually isotropic; however, a multiphase composite can be either isotropic (for majority of particular composites) or anisotropic (for instance in case of fibrous composites reinforced with directionally oriented fiber beam).…”

“…Among the variety of papers dealing with modeling of effective mechanical properties of composites and their experimental verification, the following group of papers in which a coupling between the topology of fibrous reinforcement (or particle) reinforcement and material symmetry of constitutive model describing composite can be distinguished, for instance: Sun and Vaidya [30], Gan et al [9], Liu et al [19], Würkner et al [37], Selvadurai and Nikopour [28] and others.…”

“…More systematic analysis of the influence of homogenization methods on estimated effective properties of composites is due to Gan et al [9]. The authors compare the new Strain-Compatible Method of Cells (SCMC) with other homogenization methods such as Generalized Method of Cells (GMC) Paley and Aboudi [25] and micromechanical analysis using FEM.…”

“…In corresponding elasticity matrices, compliance or stiffness, Rabinovich η 12(k) and Chencov μ 31(23) 32 . These equivalent anisotropy constants of composite have to be either measured in appropriate 9 tests or estimated by the use of a chosen homogenization method for assumed perpendicular fiber arrangements (see for instance Gan et al [9] for Boron/Al composite)…”