Numerical fatigue damage analysis and mathematical modeling of articular cartilage under cyclic load via hyperelasticity theory

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.