形状记忆合金纤维复合材料的等效力学行为

在Aboudi提出的胞元模型以及Liu等建立的形状记忆合金的本构模型的基础上，由Legendre多项式，假设每个子胞元的位移场、应变场和应力场，再由子胞元间交界面的应力连续条件和外荷载边界条件推导出基体为弹塑性材料的形状记忆合金纤维复合材料的胞元模型；模拟了呈周期对称的形状记忆合金纤维复合材料受轴向单向拉伸、横向拉伸和横向剪切荷载作用下的等效力学行为，与有限元解进行了比较，结果基本一致。与有限元法比较起来，本文推导出的形状记忆合金纤维复合材料的胞元模型更具高效性。

Equal-effective mechanical behavior of Shape Memory Alloys fiber-reinforced composite

Based on the cell models for elastic-viscoplastic composite proposed by Aboudi and Shape Memory Alloys (SMAs) constitutive model established by Liu,etc., the models of cells are derived for SMA fiber-reinforced composite, in which the matrix is assumed to be elastic-plastic work-hardening materials and SMAs fibers are imbedded in the matrix in the form of a double periodic array. In terms of the Legendre polynomials, the displacement distribution, strain field and stress field in each subcell are given. The displacements and stress components along the interfaces of subcells are considered to be continuous, and load boundary conditions which applied in the subcells is also formulated. On such basis, the relation of average stress and strain for SMAs fiber-reinforced composites are obtained, furthermore the equal-effective behavior of periodic symmetrical SMA fibrous composite material under axial tension, transverse tension and transverse shear are simulated. The result of cell models is in agreement with finite element results by comparison, however cell models for Shape Memory Alloys fiber-reinforced composites derived in this paper are more efficient than finite element method.