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.

使用分析/半分析微力学方法对异质材料的机械性能进行均质化的计算成本低于通过数值技术实现的均质化。然而，分析方法不能容易地应用于晶胞（或代表性体积元素）中微观结构的复杂分布。在这里，我们通过在傅立叶级数方法（FSA）中容纳长方体和楔形子体积来减轻这种情况。这类似于在5维有限元分析（FEA）中使用五面体和六面体元素离散几何。该技术用于研究方形，圆形和星形纤维的单向纤维/纱线增强复合材料对横向载荷的弹塑性响应。结果表明：（i）预测的横向弹性模量和剪切模量对纤维形状和晶胞构型敏感；（ii）均质复合材料的应力-应变曲线与文献中报道的一致，即使用FEA，以及（iii）目前计算出的平纹和2/2斜纹编织织物的弹性常数与其他方法得出的弹性常数相近，并且可以从测试数据中得出。在FSA中实施了基于可塑性方法的线性软化模型，以预测纱线和树脂的破坏和逐渐软化。它捕获了非线性响应，并在拉伸载荷下提供了极限强度。（ii）均质复合材料的应力-应变曲线与使用有限元分析发现的文献报道的一致，并且（iii）目前计算出的平纹和2/2斜纹编织织物的弹性常数接近于其他织物方法并从测试数据中推导出来。在FSA中实施了基于可塑性方法的线性软化模型，以预测纱线和树脂的破坏和逐渐软化。它捕获了非线性响应，并在拉伸载荷下提供了极限强度。（ii）均质复合材料的应力-应变曲线与使用有限元分析发现的文献报道的一致，并且（iii）目前计算出的平纹和2/2斜纹编织织物的弹性常数接近于其他织物方法并从测试数据中推导出来。在FSA中实施了基于可塑性方法的线性软化模型，以预测纱线和树脂的破坏和逐渐软化。它捕获了非线性响应，并在拉伸载荷下提供了极限强度。在FSA中实施了基于可塑性方法的线性软化模型，以预测纱线和树脂的破坏和逐渐软化。它捕获了非线性响应，并在拉伸载荷下提供了极限强度。在FSA中实施了基于可塑性方法的线性软化模型，以预测纱线和树脂的破坏和逐渐软化。它捕获了非线性响应，并在拉伸载荷下提供了极限强度。