that makes the prediction of viscoelastic relaxation moduli easy . the numerical example was presented in the end of this paper 给出的单向纤维复合材料的粘弹性松弛模量预测的数值算例验证了该方法的有效性。
the viscoelastic relaxation moduli in time domain are obtained by the inverse laplace transform of the curve-fitted formulae . the method takes advantage of rational curve-fitted formulae and avoids complicated numerical inverse laplace transform 该方法利用合理的曲线拟合函数避开了复杂的数值laplace逆变换,使得单向纤维增强复合材料的粘弹性性能的确定变得容易。
by laplace transforming the governing equation of the problem of unidirectional fiber reinforced composite materials, the formulae for predicting the viscoelastic relaxation moduli in laplace transformed domain are obtained . according to correspondence principle of viscoellastic mechanics and elastic, mechanics, the results of effective moduli for several s are obtained by using the finite element method of the homogenization . then effective relaxation moduli should be curve-fitted, according to the viscoelastic relaxation modulus formulae of many viscoelastic materials 首先对单向纤维增强复合材料粘弹性问题的控制方程进行laplace变换,在像空间s中利用均匀化理论建立宏观松弛模量的laplace变换泛函形式,根据粘弹性-弹性对应原理,用均匀化问题的有限元方法预报单向纤维增强复合材料在相空间中多个离散点的本构关系,然后根据典型粘弹性材料的松弛模量具有的函数形式进行曲线拟合,再通过对拟合出的函数进行laplace逆变换,从而再回到时间t域,就得到了单向纤维增强复合材料的松弛模量。
by laplace transforming the governing equation of the problem of unidirectional fiber reinforced composite materials, the formulae for predicting the viscoelastic relaxation moduli in laplace transformed domain are obtained . according to correspondence principle of viscoellastic mechanics and elastic, mechanics, the results of effective moduli for several s are obtained by using the finite element method of the homogenization . then effective relaxation moduli should be curve-fitted, according to the viscoelastic relaxation modulus formulae of many viscoelastic materials 首先对单向纤维增强复合材料粘弹性问题的控制方程进行laplace变换,在像空间s中利用均匀化理论建立宏观松弛模量的laplace变换泛函形式,根据粘弹性-弹性对应原理,用均匀化问题的有限元方法预报单向纤维增强复合材料在相空间中多个离散点的本构关系,然后根据典型粘弹性材料的松弛模量具有的函数形式进行曲线拟合,再通过对拟合出的函数进行laplace逆变换,从而再回到时间t域,就得到了单向纤维增强复合材料的松弛模量。
and then the brief description of the researches in micro-mechanics is presented . ( see chapter 1 ) 2 . the basic conception of the homogenization theory is given, and then by laplace transforming, the formulae for predicting the viscoelastic relaxation moduli in laplace transformed domain are obtained from the governing equation of the problem of composite materials (详见第一章)2、在简要介绍细观多尺度均匀化方法的基本理论的基础上,通过复合材料粘弹性问题的控制方程的laplace变换,并利用对应原理,在像空间中导出了利用均匀化理论预测宏观松弛模量的laplace变换泛函形式。