Troyer Kevin L, Shetye Snehal S, Puttlitz Christian M
Department of Mechanical Engineering, Colorado State University, Fort Collins, CO 80523-1374, USA.
J Biomech Eng. 2012 Nov;134(11):114501. doi: 10.1115/1.4007630.
Finite element (FE) models of articular joint structures do not typically implement the fully nonlinear viscoelastic behavior of the soft connective tissue components. Instead, contemporary whole joint FE models usually represent the transient soft tissue behavior with significantly simplified formulations that are computationally tractable. The resultant fidelity of these models is greatly compromised with respect to predictions under temporally varying static and dynamic loading regimes. In addition, models based upon experimentally derived nonlinear viscoelastic coefficients that do not account for the transient behavior during the loading event(s) may further reduce the model's predictive accuracy. The current study provides the derivation and validation of a novel, phenomenological nonlinear viscoelastic formulation (based on the single integral nonlinear superposition formulation) that can be directly inputted into FE algorithms. This formulation and an accompanying experimental characterization technique, which incorporates relaxation manifested during the loading period of stress relaxation experiments, is compared to a previously published characterization method and validated against an independent analytical model. The results demonstrated that the static and dynamic FE approximations are in good agreement with the analytical solution. Additionally, the predictive accuracy of these approximations was observed to be highly dependent upon the experimental characterization technique. It is expected that implementation of the novel, computationally tractable nonlinear viscoelastic formulation and associated experimental characterization technique presented in the current study will greatly improve the predictive accuracy of the individual connective tissue components for whole joint FE simulations subjected to static and dynamic loading regimes.
关节结构的有限元（FE）模型通常并未体现出软结缔组织成分的完全非线性粘弹性行为。相反，当代的全关节FE模型通常用计算上易于处理的显著简化公式来表示软组织的瞬态行为。在随时间变化的静态和动态加载条件下，这些模型的预测结果的逼真度会大大降低。此外，基于实验得出的非线性粘弹性系数但未考虑加载过程中瞬态行为的模型可能会进一步降低模型的预测准确性。当前的研究提供了一种新颖的唯象非线性粘弹性公式（基于单积分非线性叠加公式）的推导和验证，该公式可直接输入到FE算法中。将此公式以及一种伴随的实验表征技术（该技术纳入了应力松弛实验加载期表现出的松弛现象）与之前发表的表征方法进行比较，并针对一个独立的解析模型进行验证。结果表明，静态和动态FE近似值与解析解吻合良好。此外，观察到这些近似值的预测准确性高度依赖于实验表征技术。预计当前研究中提出的新颖的、计算上易于处理的非线性粘弹性公式和相关实验表征技术的实施，将大大提高全关节FE模拟中单个结缔组织成分在静态和动态加载条件下的预测准确性。
