Prediction of elastic moduli and ultimate strength of fiber/yarn-reinforced elastic–plastic matrix using Fourier series approach and cuboidal/wedge sub-volumes

Abstract

Homogenization of mechanical properties of a heterogeneous material using analytical/semi-analytical micromechanics approaches is computationally less expensive than that through numerical techniques. However, analytical methods cannot be easily applied to a complex distribution of the microstructure in a unit cell (or a representative volume element). Here, we alleviate this by accommodating cuboidal and wedge shaped sub-volumes in the Fourier series approach (FSA). This is akin to using penta- and hexa-hedral elements to discretize the geometry in 3-dimensional finite element analysis (FEA). The technique is applied to study the elasto-plastic response of unidirectional fiber/yarn-reinforced composites with square, circular and star shaped fibers to transverse loading. It is shown that (i) predicted transverse elastic modulus and the shear moduli are sensitive to the fiber shape and the unit cell configuration, (ii) the stress–strain curves for the homogenized composite agree with those reported in the literature found by using the FEA, and (iii) the presently computed elastic constants for plain and 2/2 twill weave fabrics are close to those found by other methods and deduced from the test data. A linear softening model based on plasticity approach is implemented within the FSA to predict failure and progressive softening in the yarn and the resin. It captures the nonlinear response and provides the ultimate strength under tensile loading.