Introduction
Lumbar disc herniation (LDH) is the main clinical cause of low back pain, which is usually caused by the prolapse of the nucleus pulposus through ruptured annulus fibrosus [
1]. The pathogenesis of lumbar disc herniation is very complex, and its principle is still uncertain, but the occurrence of disc rupture often accompanies it [
2]. Normally, it is caused by the accumulation of long-term mechanical load on the lumbar intervertebral disc and the sudden overload injury [
3]. In general, there are two types of structural failures exhibited in intervertebral disc: endplate fracture and annulus fibrosus rupture [
4]. These fissures do not seem to cause pain in the early stages, but they have been shown to aggravate the degeneration of the intervertebral disc [
5]. Wade et al. experimented with different loading positions for sheep lumbar vertebrae containing preexisting defects in the central dorsal annulus, and by comparing the results of scanning the intervertebral discs in ultrahigh-field MRI (magnetic resonance imaging, 11.7T) before and after the test, they found that they contained a greater degree of preexisting damage and were more prone to herniated discs [
6]. Loading rate and posture are key factors in the herniation process [
7], previous studies have shown that vertical compression often leads to endplate fractures or vertebral body injuries, and flexion increases the likelihood of annular failure, while the accuracy of the failure depends on the loading rate [
8]. For instance, Wade et al. carried out loading experiments with sheep lumbar spine at different speeds and observed the microstructure of the damaged intervertebral disc. They hypothesized the location of the initiation of annulus fibrous rupture and the mode of diffusion by comparing the categories of disc damage caused by different loads, at the same time, it also reflects that the loading rate also affects the rupture of the intervertebral disc [
9]. LI et al. carried out low, medium and high-rate loading of the intervertebral disc, and after observing the mechanical differences in intervertebral disc rupture, they pointed out that the yield phenomenon will occur at these three speeds, but the rupture phenomenon only occurs at medium and high-speed loading [
10]. Although many studies have been performed on how the intervertebral disc fails under various conditions, the mechanism of disc failure and herniation is still not fully understood.
Lumbar discs are viscoelastic in nature and can therefore exhibit different mechanical responses to different strain rates [
11]. For instance, Wade et al. conducted compression rupture experiments on sheep lumbar spine at high loading speed and found motion segments subjected to a “surprise” loading rate are likely to fail via some form of annular rupture. Failure under such sudden loading occurs mostly via rupture of the annular-endplate junction and is thought to arise from a rate-induced mechanostructural imbalance between the annulus and the endplate [
12]. In daily life, the human body will inevitably encounter falls, slips, and other conditions. In order to explore the potential pathogenesis of the above conditions that may lead to lumbar disc herniation, in 4 recent years, some scholars have studied the mechanical behavior of lumbar intervertebral discs at high loading rates [
13,
14], the above studies indicate that loading rate has an influence on disc failure mode, however, differences in experimental equipment, loading protocol, and specimens result in a lack of comparability. Therefore, the relationship between loading rate and failure mechanics is not yet well defined.
The physically realistic constitutive representation is considered as an important method to deeply understand the origin of the deformation-induced failure mechanisms affecting the IVD function [
15]. In recent years, a lot of fully three-dimensional AF model have been developed to predict the regional anisotropic multiaxial damage of the IVD with the finite element method [
16,
17], and using 3D printing technology to construct an intervertebral disc model, the model provides a convenient experimental platform for evaluating normal and pathological disc states and assessing the biomechanics of potential therapeutic interventions [
18,
19]. However, a complete constitutive model of IVD is not established above studies. The ZWT nonlinear viscoelastic constitutive model is composed of a nonlinear spring and two Maxwell elements in parallel, and a series of existing experimental studies have shown that this model can be used to satisfactorily describe the nonlinear viscoelastic constitutive behavior of various polymers within the strain rates range from 10
−4/s to 10
3/s. For example, Jiang et al. satisfactorily described the behavior of ethylene propylene diene monomer (EPDM) in 27% strain under low strain rates of 0.00025 s
−1, 0.025 s
−1 and high strain rates in the range of 1300 s
−1, 2100s
−1 using the improved ZWT nonlinear viscoelastic constitutive model [
20]. Luo et al. performed a numerical simulation of the performance of epoxy resin with a split Hopkinson pressure bar (SHPB), and the simulated stress–strain curve was in good agreement with the experimental results under quasi-static compression of 1 × 10
−4 s
−1, 1 × 10
−3 s
−1, and 1 × 10
−4 s
−1, and a high strain rate of 650 s
−1, 1050 s
−1, and 1600 s
−1. The results show that the ZWT constitutive model can better simulate the stress–strain relationship of epoxy resin in the 8% strain range and at different strain rate [
21]. Zhang et al. established the dynamic constitutive model of desert sand concrete at room temperature on the basis of the ZWT constitutive model, which can better predict the stress–strain curve in the 1.25% strain range under the dynamic compression test with strain rate of 1.45 × 10
−6 s
−1, 1.45 × 10
−5 s
−1, and 1.45 × 10
−4 s
−1 [
22]. In this article, the ZWT constitutive model is used to quantitatively describe the viscoelastic mechanical behavior of lumbar disc at high strain rate, and the physical meaning of the model parameters is thoroughly analyzed.
Conclusion
In summary, the research results indicate that compared with healthy IVD, the elastic modulus, elastic limit, and ultimate strength of injured lumbar IVD are significantly reduced, and the stress–strain curve of damaged specimens is more prone to collapse. Under quasi-static loading conditions, the strengthening stage of the IVD becomes shorter at high loading rates, and the resistance to failure is significantly reduced. In addition, as the strain rate increases, the elastic limit and ultimate strength of both healthy and damaged IVD show an increasing trend. The elastic modulus of healthy discs significantly increases, while the elastic modulus of damaged IVD significantly decreases. The high loading rate hardly affects the axial displacement of the fiber ring and the overall distribution of axial radial displacement in the forward bending state, but has a significant impact on the internal radial displacement distribution of the posterior fiber ring. MRI images indicate that injuries and high loading rates are more likely to cause disc herniation. The ZWT constitutive equation can well express the stress–strain relationship of IVD under high loading rates. Therefore, the research content of this article reflects the impact of injuries and high loading rates on IVD rupture in daily life, providing theoretical support for the prevention and treatment of LDH.
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