Modified Kelvin-Voigt Model Research Articles

A modified parametric model to predict visco-elastic properties of magneto-rheological elastomers at non-LVE region

The magneto-rheological elastomer is mostly used in vibration isolation, for which higher modulus and lower Payne effect factors are crucial parameters. Strain amplitudes and frequencies influence many applications under dynamic modes. In this work, the dynamic viscoelastic properties of MRE, fabricated using electrolyte iron (EI) particles, were measured for varying strain amplitude, magnetic field and frequency. A fractional Kelvin-Voigt (KV) model is used in a frequency region from 0.01 to 40 Hz to predict the rheological behaviour. However, the available models failed to explain the observed behaviour at low frequencies and high magnetic fields and increasing strain amplitude (i.e. in the non-viscoelastic region). Therefore, a new modified KV model is proposed in this work to incorporate the drawbacks and hence can validate for varying frequency, magnetic field and strain amplitudes. The added terms can also be used in the fractional derivative Maxwell model to explain the effect of strain amplitude and magnetic field at various frequencies. The proposed model significantly improves the quality of experimental prediction in the low-frequency range, corresponding to a slow dissipative process at different strain amplitudes.

Pullback attractors for weak solution to modified Kelvin-Voigt model

<p style='text-indent:20px;'>The paper is devoted to the investigation of the qualitative dynamics of weak solutions for the modified Kelvin-Voigt model on the base of the theory of pullback attractors for trajectory spaces. At first, for the studied model, an auxiliary problem is considered, its solvability in the weak sense is proved, and some solution estimates are established. Then, on the base of these estimates, a family of trajectory spaces is determined and the existence of trajectory and minimal pullback attractors for the considered trajectory spaces is proved.</p>

The theoretical modeling of the dynamic compaction process of forest soil.

Due to the growing demand for timber, forest soils are increasingly exposed to mechanical disturbances, caused by forestry equipment. Even though using skidding machines to transport wood is detrimental to the physical state of the soil, this method remains the most common. Hence, there is a need to model the impact of skidding systems on the upper (fertile) layer of the soil. This study aims to develop such a model using the D'Alembert principle, the method of Laplace transforms, and a modified Kelvin-Voigt model. The work shows that subdividing the tractor-bundle-soil system makes it possible to consider the dynamic effect of the vibrating tractor on the soil and soil's ability to undergo deformation separately. In addition, the study developed individual models for the first subsystem that determine vibration effects on soil caused by an unloaded tractor and two loaded skidding systems using different methods of semi-suspended skidding. The present findings can be used to predict the degree of dynamic soil compaction without conducting direct on-site experiments and thus minimize the negative impact of forestry operations on the local ecosystem. The current data also allow simplifying design models for complex forwarders.

Feedback Control Problem for Modified Kelvin-Voigt Model

This paper deals with the optimal feedback control problem for the modified Kelvin-Voigt model. The considered model describes the motion of weakly concentrated aqueous polymer solutions. In our case, the control function (the external force) depends on the velocity of the fluid. In such a way, the control is not selected from a finite set of available controls, but belongs to the image of some multi-valued map. The solution for the control problem of fluid motion is a pair: the velocity of the fluid and the control (the density of external forces). Since there can be many such pairs, the concept of optimal solution naturally arises, which gives a minimum to specified cost functional. For the considered optimal feedback control problem the existence theorem on weak solution is proved.

Control of Insertion of Indenter into Viscoelastic Tissue using a Piezoelectric Drive

Stereotactic operations are actively used in modern minimally invasive medicine. During such operations, a flexible needle is inserted into the internal organs, with the help of which a biopsy or a local treatment is performed. The applica tion of such approaches in neurosurgery requires the accurate positioning of the needle tip at the target point. The present study is related to the creation of a robotic system that delivers the needle to a given point and uses drives compatible with magnetic resonance imaging devices that visualize the position of the needle. In this paper, we propose a finite-dimensional mathematical model of a mechatronic system that uses a piezoelectric drive (PED) to move the needle (cannula) along a given line. To describe the contact between the cannula and the soft tissue, a mathematical model of their interaction is developed. The contact problem involving two processes occurring during the introduction of the needle into the biological tissue is solved: the introduction of a rigid (compared to the tissue) indenter and its retention at a certain depth. Relaxation properties of the tissue are taken into account. The behavior of tissue is described using a phenomenological approach based on a modified Kelvin-Voigt model. This allowed for reducing the solution of the contact problem to the integration of a system of ordinary differential equations. One of recognized ways to develop medical robotic systems is to test their functioning using phantoms of biological tissues. For this purpose, a phantom of a porcine brain based on agar-agar is made. Experiments are carried out to indent a standard cannula into the phantom body. Based on the obtained experimental data, the parameters of the contact model are identified. An algorithm is proposed for controlling the PED frequency, which ensures the introduction of the cannula into the soft biological tissue to a given depth. Numerical simulation of the insertion of the cannula into the soft tissue using this algorithm is performed. The influence of feedback coefficients on the position and speed of the indenter on the nature of the implementation process is investigated.

The existence theorem for weak solution of optimal feedback control problem for the modified Kelvin-Voigt model of weakly concentrated aqueous polymer solutions

In this paper the existence theorem on weak solution of the optimal feedback control problem for the modified Kelvin-Voigt model of weakly concentrated aqueous polymer solutions. The proof is carried out on the basis of an approximation-topological approach to the study of fluid dynamic problems. At the first step, the considered feedback control problem is interpreted as an operator inclusion with a multi-valued right-hand side. In the second step, the resulting inclusion is approximated by an operator inclusion with better properties. Then, on the basis of a priori estimates of solutions and the degree theory of a class of multi-valued mappings, the existence of solutions for this inclusion is proved. In the third step, it is shown that from the sequence of solutions of the approximation inclusion one can extract a subsequence that converges weakly to the solution of the original inclusion. Then it is proved that among the solutions of the considered problem there is a solution that gives a minimum to a given quality functional.

Use of flexible sensor to characterize biomechanics of canine skin

BackgroundSuture materials and techniques are frequently evaluated in ex vivo studies by comparing tensile strengths. However, the direct measurement techniques to obtain the tensile forces in canine skin are not available, and, therefore, the conditions suture lines undergo is unknown. A soft elastomeric capacitor is used to monitor deformation in the skin over time by sensing strain. This sensor was applied to a sample of canine skin to evaluate its capacity to sense strain in the sample while loaded in a dynamic material testing machine. The measured strain of the sensor was compared with the strain measured by the dynamic testing machine. The sample of skin was evaluated with and without the sensor adhered.ResultsIn this study, the soft elastomeric capacitor was able to measure strain and a correlation was made to stress using a modified Kelvin-Voigt model for the canine skin sample. The sensor significantly increases the stiffness of canine skin when applied which required the derivation of mechanical models for interpretation of the results.ConclusionsFlexible sensors can be applied to canine skin to investigate the inherent biomechanical properties. These sensors need to be lightweight and highly elastic to avoid interference with the stress across a suture line. The sensor studied here serves as a prototype for future sensor development and has demonstrated that a lightweight highly elastic sensor is needed to decrease the effect on the sensor/skin construct. Further studies are required for biomechanical characterization of canine skin.