A sign control method for fitting and interconverting material functions for linearly viscoelastic solids

被引:63
作者
Bradshaw R.D. [1 ]
Brinson L.C. [1 ]
机构
[1] Department of Mechanical Engineering, Northwestern University, Evanston
关键词
Composites; Interconversion; Linear viscoelasticity; Material functions; Multidata method; Prony series; Spectrum methods;
D O I
10.1023/A:1009772018066
中图分类号
学科分类号
摘要
The multidata method was originally proposed to fit a Prony exponential series function to experimental viscoelastic modulus and compliance data; this was accomplished by the application of a linear least squares solver. This paper considers a similar approach, but extended in two key ways. First, it has been applied to the solution of convolution integral equations; specifically those used for material function interconversion. Second, it has been modified to force the signs of the Prony series coefficients to be positive; this is an essential criterion for the proper physical interpretation of a Prony series material function, which is typically not satisfied by multidata method solutions. Sign control is implemented by an iterative Levenberg-Marquardt solution algorithm with an appropriate constraint, and can be used for both fitting experimental data and interconversion. To use the method, a Prony series must be capable of adequately representing the applicable functions. The method is demonstrated by first fitting and converting experimental modulus data. Formulation for a composite lamina is also shown, in which a system of integral equations is reduced to a single integral equation; this can then be solved using the new method. Finally, application of the new method to frequency domain transformations is demonstrated, along with comparisons to other techniques. © 1997 Kluwer Academic Publishers.
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页码:85 / 108
页数:23
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