含金属芯压电压磁纤维/聚合物基复合材料时变、非线性和多物理场响应的细观力学模型
Micromechanics modeling of time-dependent, nonlinear and multiphysics response of metal core piezoelectric and piezomagnetic fibers reinforced polymer matrix composites

为有效模拟新型多功能智能材料——金属芯压电压磁纤维/聚合物基复合材料（MPPF/PMCs）的有效时变、非线性和多物理场响应，基于变分渐近法建立增量形式的细观力学模型。首先分别导出聚合物、压电压磁材料和金属芯的增量本构关系，建立统一的本构方程；以此为基础，推导出能量变化泛函的变分表达式。考虑材料的时变和非线性特征，建立与求解瞬时切线电-磁-力耦合矩阵有关的增量过程；通过最小化近似泛函求解场变量的波动函数，并通过有限元数值实现，从而建立逼近物理和工程真实性的细观力学模型。通过含铝芯压电（BaTiO3）压磁（CoFe2O4）聚合物基复合材料算例表明：构建的模型可用于模拟不同多物理场下MPPF/PMCs的有效响应，可准确捕捉纤维与基体间的应力突变现象。 In order to effectively simulate the time-dependent, nonlinear and multiphysics response of the new type of multi-functional smart materials-metal core piezoelectric and piezomagnetic fiber reinforced polymer matrix composite (MPPF/PMC), an incremental micromechanics model was developed based on the variational asymptotic method. Firstly, the incremental constitutive equations of polymer, piezoelectric/piezomagnetic materials and metal materials were derived respectively, and a unified constitutive equation was established. Considering the time-dependent and nonlinear characteristics of composites, an incremental procedure in conjunction with an instantaneous tangential electro-magneto-mechanical matrix of composites was established. The fluctuate functions of field variables were solved by minimizing the approximate energy functional and realized by finite element method, resulting in a micromechanics model as close as possible to the physical and engineering authenticity. The numerical example of aluminum core piezoelectric (BaTiO3) and piezomagnetic (CoFe2O4) polymer matrix shows that this constructed model can be used to simulate the effective response of MPPF/PMCs under different physical fields and can accurately capture the stress mutation phenomenon between the fiber and the matrix. 国家自然科学基金（51778088）；重庆市自然科学基金（cstc2016jcyjA0426；cstc2017jcyjBX00036）