The internal stress of the human foot enables efficient parametric evaluation of structural and functional impairments associated with foot deformities, such as hallux valgus (HV). However, the status of the internal stress of such a deformed foot remains insufficiently addressed due to the difficulties and limitations of experimental approaches. This study, using finite element (FE) methodology, investigated the influence of severe HV deformity on the metatarsal stress and the metatarsophalangeal (MTP) joint loading during balanced standing. FE models of a normal foot and a severe HV were constructed and validated. Each FE model involves 28 bones and various cartilaginous structures, ligaments, and plantar fascia, as well as encapsulated soft tissue. All the materials except for the encapsulated soft tissue were considered isotropic and linearly elastic, while the encapsulated soft tissue was set as nonlinear hyperelastic. Hexahedral elements were assigned to the solid parts of bones, cartilage, and the encapsulated soft tissue. Link elements were assigned to ligaments and plantar fascia. A plate was created for simulating ground support. A vertical force of a half-body weight was applied on the bottom of the plate for simulating balanced standing loading. The superior surfaces of the encapsulated soft tissue, distal tibia, and distal fibula were fixed. Stress distribution in the metatarsals, contact pressure, and force at the MTP joints were comparatively analysed. Compared to the normal foot, the HV foot showed higher stress concentration in the metatarsals but lower magnitude of MTP joint loading. In addition, the region with high contact pressure at the first MTP joint shifted medially in the HV foot. Knowledge of this study indicates that patients with severe HV deformity are at higher risk of metatarsal injuries and functional impairment of the MTP joints while weight bearing.
The paper discusses the impact of the von Kármán type geometric nonlinearity introduced to a mathematical model of beam vibrations on the amplitude-frequency characteristics of the signal for the proposed mathematical models of beam vibrations. An attempt is made to separate vibrations of continuous mechanical systems subjected to a harmonic load from noise induced by the nonlinearity of the system by employing the principal component analysis (PCA). Straight beams lying on Winkler foundations are analysed. Differential equations are obtained based on the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Levinson-Reddy hypotheses. Solutions to linear and nonlinear differential equations are found using the principal component analysis (PCA).