The paper presents an analysis of the rheological properties of a selected viscoelastic material, which is dedicated to the reduction of vibrations in structures subjected to dynamic loads. A four-parameter, fractional Zener model was used to describe the dynamic behavior of the tested material. The model parameters were identified on the basis of laboratory tests performed at different temperatures and for different vibration frequencies. After proving that the material is thermoreologically simple, the so-called master curves were created using a horizontal shift factor. The Williams–Landel–Ferry formula was applied to create graphs of the master curves, the constants of which were determined for the selected temperature. The resulting storage and loss module functions spanned several decades in the frequency domain. The parameters of the fractional Zener model were identified by fitting the entire range of the master curves with the gradientless method (i.e., Particle Swarm Optimization), consisting in searching for the best-fitted solution in a set of feasible solutions. The parametric analysis of the obtained solutions allowed for the formulation of conclusions regarding the effectiveness of the applied rheological model.

Concrete is the most widely used construction material nowadays. We are concerned with the computational modelling and laboratory testing of high-performance concrete (HPC). The idea of HPC is to enhance the functionality and sustainability of normal concrete, especially by its greater ductility as well as higher compressive, tensile, and flexural strengths. In this paper, the influence of three types (linear displacement, uniform traction, and periodic) of boundary conditions used in numerical homogenization on the calculated values of HPC properties is determined and compared with experimental data. We take into account the softening behavior of HPC due to the development of damage (micro-cracks), which finally leads to failure. The results of numerical simulations of the HPC samples were obtained by using the Abaqus package that we supplemented with our in-house finite element method (FEM) computer programs written in Python and the homogenization toolbox Homtools. This has allowed us to better account for the nonlinear response of concrete. In studying the microstructure of HPC, we considered a two-dimensional representative volume element using the finite element method. Because of the random character of the arrangement of concrete’s components, we utilized a stochastic method to generate the representative volume element (RVE) structure. Different constitutive models were used for the components of HPC: quartz sand—linear elastic, steel fibers—ideal elastic-plastic, and cement matrix—concrete damage plasticity. The numerical results obtained are compared with our own experimental data and those from the literature, and a good agreement can be observed.

An experimental and analytical approach to the relaxation problem of wood-based materials—OSB (Oriented Strand Boards—pressed wood-based composite panels) beams, including beams with CFRP (Carbon fiber reinforced polymer) tape composite reinforcement, is presented. It is a relevant engineering and scientific problem due to the fact that wood and wood-based materials, as well as composite reinforcements, are widely used in building constructions. Their rheological properties are very important and complicated to estimate. A 10 day long relaxation test of thick OSB beams without reinforcement and with CFRP tape was performed. A four-point bending test with five different bending levels was performed, during which the reduction of the loading force was measured. A five-parameter rheological model was used to describe the rheology of the beams. The equations of this model were calculated with the use of Laplace transform, whereas the values of the parameters were calculated based on the experimental relaxation curves. A high correlation between experimental and theoretical results was obtained. A beam reinforced with CFRP tape was treated as a system with a viscoelastic element (OSB) and an elastic element (CFRP), joined together without the possibility of slipping. The equations of the mathematical model were calculated based on the assumptions of the linear theory of viscoelasticity and the convolution integral. A good correlation between experimental and theoretical results was obtained. A significant redistribution of stresses was observed during the relaxation of the reinforced beam. The reinforced beams show a higher stiffness of approximately 63% and carry proportionally higher loads than unreinforced beams at the same deflection values.

This paper presents the results of a study of polyurethane rigid (PUR) elastomers in terms of the constitutive law identification, and analyses the effect of polyurethane elastomers’ hardness on fatigue properties. The research objects were PUR materials based on 4,4′-diphenylmethane diisocyanate (MDI) with the hardness of 80 ShA and 90 ShA, typically used in various industrial applications. Based on the performed experimental campaign under static and cyclic loading, the constitutive model proposed by Ogden is most appropriate. In addition, a hybrid numerical–experimental analysis (using FEM-DIC) of diabolo specimens’ behaviour is carried out in fatigue tests. Based on the performed fatigue test, it is worth noting that the energy approach describes the fatigue process synonymously compared to the displacement or strain approach. Finally, simple fatigue characteristics were analyzed and statistically validated for both PUR material configurations.