Using the asymptotic approximation of the Maxwell element model for the analysis of stress in a conveyor belt

The features of the propagation of dynamic stresses in a conveyor belt, the material properties of which correspond to the Maxwell element model, are considered. Analytical expressions are presented for calculating the dynamic elastic modulus, the loss modulus, and the angle of mechanical loss depending on the frequency of longitudinal oscillations in the belt of an extended transport conveyor. To analyze the dynamic stress propagation process, dimensionless parameters are introduced that characterize the specific features of the viscoelastic process in a conveyor belt, the material properties of which correspond to the Maxwell element model. The transition to the dimensionless Maxwell element model is made and the analysis of the relationship between stress and deformation of a conveyor belt element for extremely large and small values of dimensionless parameters is made. The substantiation of the scope of the Maxwell element model is given. It is shown that at sufficiently high frequencies of longitudinal stress oscillations in a conveyor belt, at which the oscillation period is much less than the characteristic oscillation decay time, the relationship between stress and deformation of the conveyor belt element corresponds to Hooke's law. A qualitative analysis of the relaxation time was carried out for a conveyor belt material, the properties of which correspond to the Maxwell element model. The analysis of the propagation of dynamic stresses in the conveyor belt for the characteristic operating modes of the transport conveyor is carried out. The conveyor operating mode with a constant deformation rate of the belt element; the mode in which a constant load is suddenly applied to the belt element; the conveyor operating mode with an instantly applied load to the belt element were investigated. It was determined that in cases where the characteristic process time significantly exceeds the stress relaxation time in the conveyor belt or the longitudinal oscillation period is much less than the stress relaxation time in the conveyor belt, the Maxwell element model can be replaced with a sufficient degree of accuracy by the Hooke element model.

Analysis of stress in the conveyor belt (Maxwell–element model)

longitudinal dynamic stresses and investigate the peculiarities of the propagation of dynamic stresses along the route of material transportation. Methodology. To calculate the value of static and dynamic stresses arising in the conveyor belt, the apparatus of mathematical physics was used. Findings. A wave equation is written that determines the propagation of longitudinal vibrations in a conveyor belt, the material of which corresponds to the Maxwell-element model. An expression is obtained for calculating the speed of propagation of elastic vibrations along the conveyor belt, the frequency of vibrations and their wavelength. The characteristic relaxation time of disturbances is determined. The method of successive approximation was used to solve the wave equation. The estimation of the characteristic time of acceleration of the conveyor belt, at which there is no destruction of the material of the conveyor belt, is given. Originality. PDE-models of conveyor-type transport systems are improved, which are used to design belt speed control systems under restrictions on speed control modes. It is shown that under the modes of acceleration or deceleration of the conveyor belt, the effects associated with the occurrence and propagation of dynamic stresses along the conveyor belt, due to the characteristics of the material corresponding to the Maxwell-element model, are insignificant. Practical value. The results obtained make it possible to determine the limitations on the modes of acceleration or deceleration of the conveyor belt, preventing its damage and increased wear. This opens up prospects for designing effective control systems for the parameters of a conveyor belt, unevenly loaded with material along the transport route.

Human lung extracellular matrix hydrogels resemble the stiffness and viscoelasticity of native lung tissue

Chronic lung diseases such as idiopathic pulmonary fibrosis (IPF) and chronic obstructive pulmonary disease (COPD) are associated with changes in extracellular matrix (ECM) composition and abundance affecting the mechanical properties of the lung. This study aimed to generate ECM hydrogels from control, severe COPD [Global Initiative for Chronic Obstructive Lung Disease (GOLD) IV], and fibrotic human lung tissue and evaluate whether their stiffness and viscoelastic properties were reflective of native tissue. For hydrogel generation, control, COPD GOLD IV, and fibrotic human lung tissues were decellularized, lyophilized, ground into powder, porcine pepsin solubilized, buffered with PBS, and gelled at 37°C. Rheological properties from tissues and hydrogels were assessed with a low-load compression tester measuring the stiffness and viscoelastic properties in terms of a generalized Maxwell model representing phases of viscoelastic relaxation. The ECM hydrogels had a greater stress relaxation than tissues. ECM hydrogels required three Maxwell elements with slightly faster relaxation times (τ) than that of native tissue, which required four elements. The relative importance (Ri) of the first Maxwell element contributed the most in ECM hydrogels, whereas for tissue the contribution was spread over all four elements. IPF tissue had a longer-lasting fourth element with a higher Ri than the other tissues, and IPF ECM hydrogels did require a fourth Maxwell element, in contrast to all other ECM hydrogels. This study shows that hydrogels composed of native human lung ECM can be generated. Stiffness of ECM hydrogels resembled that of whole tissue, while viscoelasticity differed.

Shock Mechanics Model and Characteristic Analysis of Polyurethane Isolator with Displacement Restrictor

Vibration isolator with displacement restrictor is used to best control vibration and shock simultaneously. This can’t be realized without a proper mechanics model. The drop weight test on the polyurethane isolator with displacement restrictor was discussed. The generalized mechanics model of vibration isolator based on the MAXWELL element and gap element was established, which can help the shock characteristics analysis and parameter optimization of the isolator.

Three-Parameter Viscoelasticity Models for Ballistic Fabrics

Ballistic fabrics are made from high performance polymeric fibers such as Kevlar®, Twaron® and Spectra®. These fibers often behave viscoelastically in high strain rate deformations. The Kelvin-Voigt and Maxwell rheological models have been used to characterize such viscoelastic responses at different strain rates. However, these two-parameter models have been found to be inadequate and inaccurate in some applications. As a result, three-parameter rheological models have been utilized to develop constitutive relations for viscoelastic polymeric fabrics. In this study, a generalized Maxwell (GM) model and a generalized Kelvin-Voigt (GKV) model are proposed to describe the viscoelastic behavior of a ballistic fabric, Twaron® CT716, at the strain rates of 1 s−1 and 495 s−1. The GM model consists of a Maxwell element (including a viscous dashpot and a spring in series) and a second spring in parallel to the Maxwell element, while the GKV model is an assembly of a Kelvin-Voigt (KV) element (containing a viscous dashpot and a spring in parallel) and a second spring in series with the KV element. The predictions by the GM and GKV models are compared with existing experimental data, which shows that the two sets of results are in fairly good agreement. In particular, the comparison reveals that the GKV model gives more accurate results at the low strain rate, whereas the GM model performs better at the high strain rate while still providing accurate predictions for the low strain rate responses.

Modeling of Visco-Hyperelastic Behavior of Foams

In this paper, a new visco-hyperelastic constitutive law for describing the rate dependent behavior of foams is proposed. The proposed model was based on a phenomenological Zener model: a hyperelastic equilibrium spring, which describes the steady-state, long-term response, parallel to a Maxwell element, which captures the ratedependency. A nonlinear viscous damper connected in series to a hyperelastic intermediate spring, controls the ratedependency of the Maxwell element. Therefore, the stress is the sum of equilibrium stress on the equilibrium spring and overstress on the intermediate spring. In hyperelastic theory stress is not calculated directly as in the case of small-strain, linear elastic materials. Instead, stresses are derived from the principle of virtual work using the stored strain energy potential function. In addition, foams are compressible, therefore classic strain energy functions such as the Ogden strain energy function or the Mooney-Rivlin strain energy function are not suitable to describe hyperelastic behavior of foams. So, strain energy functions must include the effect of compressibility. That means the third principal invariant of the deformation gradient tensor F should enter in strain energy functions. For rate-dependent behavior of foams, history integral constitutive law is used. For the equilibrium spring and the intermediate spring, the same strain energy function is employed. In order to use this stain energy function in history integral equation, the kernel function of it is calculated. The effect of compressibility is considered in rate-dependent behavior of foams too. All material constants were obtained from the results of uniaxial tensile tests. Nonlinear regulation was used to find these constants. In these calculations, Average strain rate was employed to find material constants.