Computation of the linear viscoelastic relaxation spectrum from experimental data

A unified procedure for rapidly determining asphalt concrete discrete relaxation and retardation spectra

“…Emri and Tschoegl [12] and Tschoegl and Emri [13] proposed a novel recursive algorithm considering the graphical characteristics of the exponential and Lorentzian kernel functions. Other methods were reported to resolve the ill-posed (i.e., non-unique) issues during the spectral identification, e.g., the Tikhonov regularization method [14], the quadratic programming regularization method [15] and the maximum entropy method [16]. In addition, given that the discrete relaxation and retardation spectra are mathematically equivalent [4], some researchers indirectly obtained one discrete spectrum from the other by using different inter-conversion methods [17][18][19][20][21][22].…”

An Approach to the Determination of the Deformation Characteristics of Viscoelastic Materials

“…This shortcoming is overcome by using the so-called Prony series [14] as the influence function (see [13] for a procedure of constructing this series). However, a satisfactory fit of experimental data for specific materials requires a large number of terms in such series.…”

“…D * is defined by the expression (13) with the parameters (16), and E = 2.24⋅10 6 Pa. Thus, the operators (23) are viscoelastic analogs of Young's moduli and Poisson's ratios appearing in (19).…”

Computation of the linear viscoelastic relaxation spectrum from capillary viscosity data

“…In principle, [1][2][3][4][5][6][7][8][9][10][11][12][13][14] the relaxation spectrum may be determined from a number of experimentally measurable linear viscoelastic properties. However, the experimental measurements usually employed are those of the storage (GЈ) and loss (GЉ) moduli obtained from oscillatory shear experiments.…”

“…It is well known that solving for H() is an ill-posed problem, and during the last [16][17] decade several improved numerical methods have been proposed for its solution. These methods employ either regression techniques (linear or non-1-2 linear) or regularization techniques and their [3][4][5][6][7][8][9][10] merits and shortcomings have been extensively discussed in the literature. 14 The objective of this work is to demonstrate the estimation of the relaxation time spectrum from capillary steady shear and extensional data by using a modification of the Leonov constitutive equation and to discuss the validity and potential limitations of the proposed methodology.…”