Nonlinear viscoelasticty plays an essential role in the functional behavior of spinal ligaments

Biomechanical behavior of bovine periodontal ligament: Experimental tests and constitutive model

“…To obtain unique fitted viscous parameters, it is necessary to fix the relaxation times (Troyer and Puttlitz, 2012). For this purpose, the constant relaxation times were considered (τ 1 ¼ 0:1, τ 2 ¼ 1, τ 3 ¼ 10 and τ 4 ¼ 100 s).…”

“…The majority of viscoelastic constitutive models of the PDL, like other biological tissues, were proposed based on Fung's (1993) quasi-linear viscoelastic (QLV) formulation (Toms et al, 2002). Although this formulation is one of the most well-known constitutive models in the field of the biomechanics, nevertheless, has an important drawback: it is unable to describe the nonlinear viscous phenomena (Provenzano et al, 2002;Troyer and Puttlitz, 2012). Other papers, like Zhurov et al (2007) proposed a transversely isotropic viscohyperelastic constitutive model with 17 invariants by defining a viscous energy function which involved time derivative of the right Cauchy-Green deformation tensor.…”

Biomechanics of the L5–S1 motion segment after total disc replacement – Influence of iatrogenic distraction, implant positioning and preoperative disc height on the range of motion and loading of facet joints

“…However, only one material composition (Table 1) was selected, although the material characteristics can vary between subjects and by the degree of degeneration. Furthermore, spinal ligaments were simplified as tension-only spring elements with nonlinear elastic behavior, although they show a viscoelastic behavior in experimental studies, which decreases part of the load over time (Troyer 2012). However, this simplification will not qualitatively alter the presented order of sensitivities.…”

Experimental Characterization and Finite Element Implementation of Soft Tissue Nonlinear Viscoelasticity

“…The time constants were fixed at decadal values that began and ended with the decade associated with the experimental ramp time and the length of the experiment, respectively [8,16,21,34]: TI=0.1S, T2=1S, T3=10s, T4=100s, Additionally, we have previously demonstrated that the form of Eq, (2) produces mathematically unique coefficients [21] and is independent of the initial guess required by the fitting algorithm [16], Stress relaxation data at each strain magnitude were fitted to Eq, (1) using two characterization techniques: (1) a novel viscoelastic characterization technique (comprehensive viscoelastic characterization, or CVC, method) that incorporates viscoelastic effects during the loading event via a computational algorithm that iterates between the experimental (finite ramping period) and the theoretical (instantaneous ramping period) stress relaxation experiment [21], and (2) a previously used characterization technique [19,32,36] wherein strain was assumed to be applied instantaneously (i.e., a Heaviside step application, thereby neglecting relaxation manifested during loading) and data fitting began after a multiple of 2,5 times the ramp time ?o (referred to herein as the 2.5to method).…”

“…For each fitting method, the strain dependence of the moduli components were determined po.st hoc via a polynomial formulation [21,31,34,37,38]:…”