2012/06/12 by Ivan Argatov, Argatov, Ivan
Engineering · Mathematics · Medicine · #74M20 #Classical Analysis and ODEs (math.CA) #Diabetic Foot Ulcer Assessment and Management #FOS: Mathematics #Knee injuries and reconstruction techniques #Lower Extremity Biomechanics and Pathologies #Orthopedic Surgery and Rehabilitation #Osteoarthritis Treatment and Mechanisms #math.CA #msc:74M20
paper · pdf · doi:10.48550/arxiv.1206.2681
31 pages, 11 figures
arxiv created 2012/06/12 · openalex publication_date 2012/06/12 · arxiv updated 2012/06/14 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28
In recent years, a number of experimental studies have been conducted to investigate the mechanical behavior and damage mechanisms of articular cartilage under impact loading. Some experimentally observed results have been explained using a non-linear viscoelastic impact model. At the same time, there is the need of simple mathematical models, which allow comparing experimental results obtained in drop impact testing with impact loads of different weights and incident velocities. The objective of this study was to investigate theoretically whether the main features of articular impact could be qualitatively predicted using a linear viscoelastic theory or the linear biphasic theory. In the present paper, exact analytical solutions are obtained for the main parameters of the Kelvin-Voigt and Maxwell impact models. Perturbation analysis of the impact process according to the standard viscoelastic solid model is performed. Asymptotic solutions are obtained for the drop weight impact test. The dependence of the coefficient of restitution on the impactor parameters has been studied in detail.