Estimation of the quasi-linear viscoelastic parameters using a genetic algorithm

Abstract

The quasi-linear viscoelastic (QLV) theory of Fung has been widely used for the modeling of viscoelastic properties of soft tissues. The essence of Fung’s approach is that the stress relaxation can be expressed in terms of the instantaneous elastic response and the reduced relaxation function. Using the Boltzmann superposition principle, the constitutive equation can be written as a convolution integral of the strain history and reduced relaxation function. In the appropriate models, QLV theory usually consists of five material parameters (two for the elastic response and three for the reduced relaxation function), which must be determined experimentally. However, to be consistent with the assumptions of QLV theory, the material functions should be obtained based on a step change in strain which is not possible to be performed experimentally. It is known that this may result in regression algorithms that converge poorly and yield non-unique solutions with highly variable constants, especially for long ramp times. In this paper, we use the genetic algorithm approach, which is an adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetics, and simultaneously fit the ramping and relaxation experimental data (on ligaments) to the QLV constitutive equation to obtain the material parameters.