预测复合材料非线性有效介电系数的割线方法

PREDICTION OF EFFECTIVE NONLINEAR SUSCEPTIBILITY OF COMPOSITES

提出了预测复合材料非线性电位移和电场强度关系的一种解析方法,该方法基于各向材料的割线介电常数,将非线性问题转化成一系列线性问题来求解。该方法适用于任意各向异性复合材料和组分材料的非线性性质,而常用的Stroud和Hui的模型只适用于各向同性复合材料和组分材料的弱线性。证明了本文方法具有PonteCastaneda提出的变分结构。计算结果表明,当基体非线性较小时,本文模型的预测与Stroud和Hui的模型一致,但当基体非线性系数增大时,本文模型能给出合理的预测结果,而Stroud和Hui的模型则会超出基体和夹杂的性能范围。

An analytical method is proposed to predict the nonlinear susceptibility of general composite materials. The method was based on the secant permittivities of each phase, and a nonlinear problem was transformed into a series of linear problems. The method is applied to any anisotropic composite and the nonlinearity of the constituents, contrary to the Stroud and Hui method, which is valid for isotropic composites and weak nonlinearity. As for the nonlinear mechanical behavior, it is shown that the proposed method is identical to the Ponte Castaneda variational method when the same method is used for the linear comparison composite. Some numerical computations are provided to illustrate the influence of the microstructure on the overall nonlinear relation between the electric displacement and the electric field.