On the Structural Origin of the Quasilinear Viscoelastic Behavior of Tissues

Abstract

Since its introduction by Fung (1972), the law of quasilinear viscoelasticity (QLV) was applied for several tissues including, among others, tendons (Haut and Little, 1972), ligaments (Geiger et al, 1983; Woo et al, 1981), articular cartilage under tension (Woo et al, 1980), heart valves (Rousseau et al, 1983), papillary muscle (Pinto and Patitucci, 1980), and smooth muscle (Price et al, 1977). Fung based the QLY law on the observation that, in several tissues, the time-varying response to a step change in uniaxial stretch $(from{\kern 1pt} \lambda = 1.0{\kern 1pt} to{\kern 1pt} \lambda > {\kern 1pt} 1.0)$, can be expressed by:

$$ \sigma (\lambda ,t) = G(t) \cdot {T^{(e)}}(\lambda ),\quad G(0) = 1, $$

(xxx)

where G(t) is the reduced relaxation function and T ^(e) (sI) is the elastic (immediate) response.