Keywords: viscoelasticity, correspondence principle, parameter identification, discrete wavelet transform, finite element analysis.

There is an increased demand for identification or back analysis in various engineering fields. Back analysis has been mainly applied for predicting unknown parameters such such as the initial stress or material properties. It is assumed that in most of these works the material is elastic. However, soil, rock mass, concrete or most materials usually show time dependency.

The elastic-viscoelastic correspondence principle [1] is that the Laplace time-transformed viscoelastic field equations and boundary conditions are formally identical with the equations for an elastic body of the same geometry. Thus, transformed solutions can be calculated using standard elastic analysis, and then inverted to obtain the time dependent response. Therefore, identification analysis of viscoelastic materials can be converted to an 'associated' elastic problem in the Laplace domain [2].

Most of the inverse problems generally require the solution of an ill-posed system of equations. Especially for a problem in which the number of unknown parameters exceeds the measured data, it is difficult to identify the unknown parameters. The wavelet transform is a mathematical tool and has been widely used for image compression and signal processing. Various finte element or boundary element techniques together with wavelet transforms have been studied for solving systems of linear equations. Doi et al. presented a new inverse method using wavelet analysis in magnetic fields [3], which utilizes the data compression ability and the spectrum resolution ability of the waveforms.

An identification scheme for elastic materials applying the wavelet transform was proposed [4]. In this paper, this scheme is adapted to the identification of viscoelastic materials. A two-dimensional discrete wavelet transform is applied to the system matrix for identifying viscoelastic materials in the Laplace domain, and then the viscoelastic parameters are identified in the real domain by applying the least-squares estimation. Finite element discretization is used for the linear viscoelastic analysis and viscoelastic parameters for volumetric and deviatoric components are sought using displacement values calculated using the ordinary finite element method as 'observed data'. A numerical example is calculated to investigate the validity of the method.

1

W. Flügge, "Viscoelasticity", Springer-Verlag, 1975.

2

T. Ohkami, J. Murai, "Identification procedure for viscoelastic materials using correspondence principle", Communications in Numerical Methods in Engineering, 14, 497-504, 1998. doi:10.1002/(SICI)1099-0887(199806)14:6<497::AID-CNM159>3.3.CO;2-U

3

T. Doi, S. Hayano, Y. Saito, "Wavelet Solution of The Inverse Source Problems", IEEE Transactions on Magnetics, 33(2), 1935-1938, 1997. doi:10.1109/20.582671

4

T. Ohkami, J. Nagao, S. Koyama, "Identification of elastic materials using wavelet transform", Computers and Structures, 84, 1866-1873, 2006. doi:10.1016/j.compstruc.2006.08.030

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £65 +P&P)