The paper presents the modeling of damage to articular cartilage under cyclic daily loads using a curved beam model and hyper-elasticity theory. Mainly, articular cartilage (AC) is a kind of very important biological tissue that has the fundamental role of withstanding applied mechanical loads and providing smooth movement of joints. The existence of mechanical loads, however, has a huge influence on the behavior and the entire healthiness of AC. These loads, over time, can cause injury through fatigue-type damage because of frequent stresses. The basic aim of this study is to mainly offer a detailed mathematical model measuring the damage caused in AC under the action of mechanical forces incorporating different variants like age, body mass index, metabolic activity, functionally graded, porosity and prestresses. The structural energies including potential energy according to the neoHookean model as well as kinetic energy and external work are achieved through the use of strain-displacement and stress-strain relations. Then, the nonlinear governing equations of the articular cartilage are derived using Hamilton's principle. Furthermore, the mathematical model has been implemented numerically through the differential quadrature method (DQM). A qualitative correspondence between the numerical predictions and experimental data has led us to conclude that this model has the potential to serve as a valuable tool for physicians and therapists. The results of this research indicate that among the factors affecting the increase of damage in cartilage, the most important factor is the body mass index, followed by a person's age, hormonal conditions, and cartilage thickness with a negative effect. The probability of damage for an athlete is about 33 percent higher than a normal person, and for a weightlifter (heavy sports) it is about 140 percent higher than a normal person.

中文翻译：

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基于超弹性理论的循环载荷下关节软骨的数值疲劳损伤分析和数学建模


本文提出了使用曲梁模型和超弹性理论对日常循环载荷下关节软骨损伤进行建模。主要是，关节软骨（AC）是一种非常重要的生物组织，具有承受机械载荷和提供关节平滑运动的基本作用。然而，机械负载的存在对空调的行为和整体健康状况有巨大影响。随着时间的推移，这些负载可能会因频繁的压力而导致疲劳型损坏，从而造成伤害。本研究的基本目的是主要提供一个详细的数学模型，测量机械力作用下交流电造成的损伤，其中包含年龄、体重指数、代谢活动、功能分级、孔隙率和预应​​力等不同变量。结构能，包括根据 NeoHookean 模型的势能以及动能和外功，是通过使用应变-位移和应力-应变关系获得的。然后，利用哈密顿原理推导了关节软骨的非线性控制方程。此外，该数学模型已通过微分求积法（DQM）进行了数值实现。数值预测和实验数据之间的定性对应关系使我们得出结论，该模型有潜力成为医生和治疗师的宝贵工具。这项研究结果表明，在影响软骨损伤增加的因素中，最重要的因素是体重指数，其次是人的年龄、荷尔蒙状况和具有负面影响的软骨厚度。 运动员受伤的概率比正常人高出约33%，举重运动员（重型运动）则比正常人高出约140%。