A simplified approach to quasi-linear viscoelastic modeling

Abstract

The fitting of quasi-linear viscoelastic (QLV) constitutive models to material data often involves somewhat cumbersome numerical convolution. A new approach to treating quasi-linearity in 1-D is described and applied to characterize the behavior of reconstituted collagen. This approach is based on a new principle for including nonlinearity and requires considerably less computation than other comparable models for both model calibration and response prediction, especially for smoothly applied stretching. Additionally, the approach allows relaxation to adapt with the strain history. The modeling approach is demonstrated through tests on pure reconstituted collagen. Sequences of "ramp-and-hold" stretching tests were applied to rectangular collagen specimens. The relaxation force data from the "hold" was used to calibrate a new "adaptive QLV model" and several models from literature, and the force data from the "ramp" was used to check the accuracy of model predictions. Additionally, the ability of the models to predict the force response on a reloading of the specimen was assessed. The "adaptive QLV model" based on this new approach predicts collagen behavior comparably to or better than existing models, with much less computation.

A Nonlinear Model of Passive Muscle Viscosity

“…It has been shown in the data presented here and elsewhere [13,14] that this is not the case for muscle. Nekouzadeh et al [32] developed an extension of the QLV model, which allows relaxation to adapt to strain history and eliminates the requirement for separability. However, both this adaptive QLV model and the original QLV model still obey superposition and thus cannot describe the response of the muscle to incremental stretches [14].…”

Viscoelastic Relaxation and Recovery of Tendon

“…A major limitation noted by others is the assumption of a linear material response, 34 manifesting itself in a single reduced relaxation function over a range of strain levels 26 or constant amplitude of viscous effects over a range of frequencies. 17 The QLV model was inaccurate at high strain rates during experiments performed by Woo et al, 35 and has also been shown by investigators to under-predict hysteresis 25,36 and early stress relaxation.…”

A discrete spectral analysis for determining quasi-linear viscoelastic properties of biological materials

“…Fung's QLV model, reviewed extensively and in more detail by others [7,8,12,14,15,18,[22][23][24][25][26][27], provides a simple strain-dependent extension of (2.2) in which the temporal decay of stress is independent of strain: (1) represents the elastic response. Based upon the concave-up force-displacement curves common to collagenous tissues, Fung proposed using an exponential relationship that he attributes to Kenedi et al [1,28] Figure 1.…”

“…However, the confidence interval for estimation of the parameters of the 'box'-shaped temporal relaxation function that Fung suggested in his book [1] are typically large [5], which complicates comparison of materials. Further, the usual box form of the temporal relaxation function is sufficiently restrictive that many have found the need to apply different relaxation functions [6][7][8] or apply different QLV representations altogether [9]. Finally, identifying when the box spectrum is too restrictive to describe a specific biological material's time-dependent mechanical responses is a challenge [3,10 -17] because, with this box spectrum, the Fung QLV model can fit relaxation data even for materials whose responses to dynamic loading it would fail to predict [18,19].…”