多相周期压电纤维复合材料反平面变形问题的解析解
An analytical solution for periodic multi-phase fibrous piezoelectric composites under antiplane deformation

研究了具有周期微结构的多相压电纤维复合材料在反平面变形下的电弹性场。通过在各非均匀相内引入非均匀的广义本征应变, 将原问题等价为带有周期广义本征应变的均匀介质问题, 建立了两者间的等价条件。利用等价问题各区域交界处的广义应力连续条件和广义位移协调条件, 并结合双准周期Riemann边值问题理论和等价条件, 获得了各相材料电弹性场的解析解, 进而由平均场理论预测了材料的有效压电系数。比较了相同压电材料体积分数下中空压电纤维、碳芯压电结构纤维和实心压电纤维复合材料有效压电系数的差异, 讨论了压电结构纤维中非压电芯刚度及压电结构纤维与基体间涂层的刚度对有效压电系数的影响。研究结果可为高灵敏度压电复合材料的设计提供有价值的参考。 The electro-elastic field of multi-phase fibrous piezoelectric composites with periodic microstructure under antiplane deformation was studied. By introducing non-uniform generalized eigen strain in each inhomogeneous phase, the original problem was replaced by a homogenous medium problem with the periodically distributed generalized eigen strains, the equivalent condition between the two problems was established. By use of the continuity conditions of generalized stress and the compatibility conditions of generalized displacement on the interfaces of each neighboring region in equivalent problem, together with doubly quasi-periodic Riemann boundary value problem theory and equivalent condition, the analytical solutions of the electro-elastic fields in each phase of composites were derived, and the effective piezoelectric coefficient of the composites was evaluated by using average field theorem. The differences of the effective piezoelectric coefficient of composites with hollow piezoelectric fibers, carbon core piezoelectric structural fibers and solid piezoelectric fibers were demonstrated under the same piezoelectric material volume fraction, and the effects of the stiffness of non-piezoelectric core in the piezoelectric structural fibers and coatings between piezoelectric structural fibers and matrix on the effective piezoelectric coefficient were discussed. The conclusions can provide valuable references for designing piezoelectric composites with high sensibility. 河北省自然科学基金(A2013203213, A2013203103)