A semi-analytical approach is proposed to determine the effective magneto-electro-elastic moduli of a fiber-reinforced composite. We especially focus on predicting the effective properties of three-phase periodic composite reinforced with unidirectional, infinitely long and concentric cylindrical fibers with square transversal distribution. The semi-analytical method is developed combining asymptotic homogenization and finite element methods. Asymptotic homogenization method allows the statements of local problems that are solved by finite element method and the associated effective coefficients. Finite element method is implemented via the principle of minimum potential energy. The effect of interphase thickness and the fiber material properties on effective moduli is analyzed. Numerical computations were performed, and an exact agreement is obtained by comparing the semi-analytical approach with asymptotic homogenization method linked to the theory of potential functions of a complex variable.

提出了一种半分析方法来确定纤维增强复合材料的有效磁电弹性模量。我们特别着重于预测具有方形横向分布的单向，无限长且同心的圆柱形纤维增强的三相周期性复合材料的有效性能。结合渐近均匀化和有限元方法开发了半分析方法。渐近均质化方法允许陈述通过有限元法和相关有效系数解决的局部问题。有限元法是通过最小势能原理实现的。分析了相间厚度和纤维材料性能对有效模量的影响。进行了数值计算