The contact problem of axial compression of an elastic, slender prismatic specimen by loading plates is considered, taking into account friction in the contact zone. The relevance of the work stems from the need for accurate evaluation of the elastic properties of materials with complex structures – such as functionally graded materials, composites, and biomaterials, where classical rod models produce systematic errors of up to 20–30 % due to neglected friction and contact effects. To solve the problem a variational approach combined with the Kantorovich method is used; this reduces the three-dimensional linear elasticity problem to a system of second-order ordinary differential equations with variable coefficients for generalized displacements. Analytical solutions are obtained for specimens with arbitrary and square cross-sections under constant elastic properties. An effective integral friction parameter is introduced – the ratio of tangential to normal generalized forces on the end faces. The inverse problem of reconstructing the elastic properties and the friction parameter from displacement data at several points on the lateral surface is solved. An iterative algorithm based on the contraction-mapping principle is developed, providing sufficiently accurate recovery of the unknown parameters in 3–5 iterations for the considered set of initial guesses. In addition, approximate asymptotic formulas based on solutions of the direct problem are proposed for rapid parameter recovery from measurements at a single point, together with recommendations for selecting measurement locations on the lateral surface. Numerical experiments on synthetic data generated by the direct problem confirm the effectiveness of the proposed methods and their robustness to noise (in the case of the iterative algorithm), demonstrating superiority over rod models. The approach enables improved processing of experimental compression test data, which is especially important for samples made of biomaterials and composites where friction significantly influences result interpretation.
The influence of a strong Allee effect in a prey population on the dynamics of a predator–prey model with ideal free distribution (IFD) is considered. A comparison of stationary solutions is given for two systems: with and without the Allee effect. It is shown that the prey always maintains its IFD, while the predator has complex IFD-like distribu-tions depending on the resource function and the Allee parameter. The presence of a strong Allee effect in the prey leads to a change in the stability of the trivial zero equilibrium and the emergence of a new unstable solution. In this case, the range of stability of the stationary state corresponding to the coexistence of two species decreases by an amount proportional to the Allee parameter and inversely proportional to the resource. It was found that changing the Allee parameter directly affects the popu-lation size of the predator (the larger the parameter, the smaller the population), while the population of the prey remains unchanged. It was found that with increasing Allee's parameter, for some points in the range (due to the dependence of the resource function on the spatial coordinate), the stationary solution with two species becomes unstable for small perturbations of the system. As a result, the population distribution contains regions where their abundance is zero. Computational experiments demonstrating the presence of an oscillatory regime for two species are presented. A system without the Allee effect maintains oscillations and the general form of its spatial distribution under small perturbations of the initial condi-tions. With a strong Allee effect, local oscillations are possible, caused by the fact that the condition for their occurrence depends on a spatially varying resource function.
The forming limit curve is a feature of the material that represents the limiting strains that lead to failure of the necking with respect to the direction of deformation strain. It displays the ductile damage & onsite necking failure limits, thickening of metal sheets that are very thin. Few-er than 100 microns, is challenging and demands greater accura-cy. Micro-forming is the term used to describe this kind of miniaturisation in the forming process, which produces components with dimensions as small as a few millimetres. When a macro process is transformed into a mi-cro process, there are significant varia-tions in the physics of the process and the characteristics of the materials. In order to identify the forming limit curves, an experimental test on a thin Nickel 200 sheet with a 50 m thickness was conducted with varied orientations to rolling directions (0°, 45°, and 90°). According to the test standard ASTM-2218-14, the hemispherical microform punch test is performed using uniaxial, intermediate-uniaxial, biaxial and plane strain specimens to determine the strains. Experimental values have been used to validate numerical find-ings. Nu-merical analysis is used to model the micro-forming process, and forming limit curves are shown. Numerical results have been validated using experimental observations.
Transcatheter aortic valve implantation (TAVI) is a minimally invasive approach for the treatment of aortic stenosis in patients with a high risk of postoperative complica-tions who are not candidates for open surgery operation. Despite the rapidly growing number of such operations, they have a number of complications with limited choice of parameters and types of implants that do not take into account the individual characteris-tics of the patient. This leads to the question of customization of TAVI implants. The de-velopment of personalized prosthetic designs can reduce the incidence of postoperative complications, such as paravavular regurgitation or damage to the annulus fibrosus, thereby improving patients’ quality of life by optimizing hemodynamic indicators. Thus, the purpose of this study is to numerically simulate the hemodynamic characteristics in the aorta after TAVI to assess the impact of the prosthesis design on its effectiveness. This paper presents eight parametrized prosthesis geometries: two represent models of commercial valves (Evolut R PRO and SAPIEN 3), and the remaining six were developed by the authors. A coupled problem involving fluid-structure interaction was solved. A velocity profile based on echocardiography data was prescribed as the inlet boundary condition at the aorta, while a pressure determined by a two-element Windkessel model was prescribed at the outlet. Based on a comprehensive analysis of the integral parame-ters, three geometries were selected. These geometries demonstrate optimal hemody-namic performance: effective orifice areas exceeding 1.5 cm², moderate pressure gradi-ents (7–12 mmHg), and peak systolic velocities below 2 m/s. Additionally, they exhibit low OSI values (OSI < 0.25), which is indicative of a reduced risk of thrombosis and prema-ture leaflet fatigue. The obtained results provide a basis for the design, engineering, and manufacture of personalized TAVI prostheses that take into account the specific anatomi-cal and physiological features of each patient.
Aim of the study was to experimentally characterize the microstructure and mechanical properties of the bovine xenopericardial patch “Neokor” modified with ethylene glycol diglycidyl ether, and to develop a hyperelastic constitutive model for finite-element simulations of the patch mechanical response. Bovine pericardium specimens (n = 7) were analyzed using small-angle light scattering (SALS) to quantify the distribution of collagen fiber orientations. Mechanical behavior was assessed under planar biaxial tension using a custom-built biaxial testing device. A series of loading protocols with different principal stretch ratios along the specimen axes was performed, and stress – stretch responses were recorded in two orthogonal directions. Combining SALS and biaxial data, parameters of an anisotropic hyperelastic Gasser – Ogden – Holzapfel model were identified, with particular emphasis on inter-specimen variability and the feasibility of using a single parameter set across the batch. Planar biaxial testing confirmed a nonlinear and anisotropic deformation response. A single fiber family model with fixed fiber dispersion provided an adequate description of the experimental data for all loading protocols: the root mean square error did not exceed 5–10 % of the maximum stress level, and the averaged parameter set reproduced the behavior of all specimens in the batch. The resulting microstructural and mechanical characteristics, together with the identified constitutive relation, can be used in computational modeling of interactions between “Neokor” xenopericardial patches and native tissues in vascular and intracardiac reconstruction, and may serve as a basis for rational selection of patch material and orientation.
