Finite deformation and fractional order viscoelasticity of an auxetic foam

2022 ◽  
pp. 1045389X2110643
Author(s):  
Eugenia Stanisauskis ◽  
Paul Miles ◽  
William Oates
Keyword(s):  
Fractional Order ◽  
Finite Deformation ◽  
Viscoelastic Behavior ◽  
Integer Order ◽  
Relaxation Effects ◽  
Viscoelastic Parameters ◽  
Rate Dependent ◽  
Improve Model ◽  
Model Predictions ◽  
And Performance

Auxetic foams exhibit novel mechanical properties due to their unique microstructure for improved energy-absorption and cavity expansion applications that have fascinated the scientific community since their inception. Given the advancements in material processing and performance of polymer open cell auxetic foams, there is a strong desire to fully understand the nonlinear rate-dependent deformation of these materials. The influence of nonlinear compressibility is introduced here along with relaxation effects to improve model predictions for different stretch rates and finite deformation regimes. The viscoelastic behavior of the material is analyzed by comparing fractional order and integer order calculus models. All results are statistically validated using maximum entropy methods to obtain Bayesian posterior densities for the hyperelastic, auxetic, and viscoelastic parameters. It is shown that fractional order viscoelasticity provides [Formula: see text]–[Formula: see text] improvement in prediction over integer order viscoelastic models when the model is calibrated at higher stretch rates where viscoelasticity is more significant.

scholarly journals Fractional Control of Coordinated Manipulators

2007 ◽  
Vol 11 (9) ◽  
pp. 1072-1078 ◽  
Author(s):  
N. M. Fonseca Ferreira ◽  
◽  
J. A. Tenreiro Machado ◽  
Keyword(s):  
Fractional Order ◽  
Force Control ◽  
Coordinated Motion ◽  
Integer Order ◽  
System Robustness ◽  
Order Position ◽  
End Effectors ◽  
And Performance ◽  
Fractional Control

When two robots execute a coordinated motion it is required specification not only of the desired trajectory of each robot, but also of the forces exerted by the end effectors. This article discusses the fractional-order position and force control of two co-operative robots handling one object. The system robustness and performance is analyzed and compared with other control approaches. The experiments reveal that fractional algorithms lead to performances superior to classical integer-order controllers.

scholarly journals Rate-Dependent Modeling of Piezoelectric Actuators for Nano Manipulation Based on Fractional Hammerstein Model

Micromachines ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 42
Author(s):  
Liu Yang ◽  
Zhongyang Zhao ◽  
Yi Zhang ◽  
Dongjie Li
Keyword(s):  
Fractional Order ◽  
Dynamic Characteristics ◽  
Autoregressive Model ◽  
Tracking Control ◽  
Piezoelectric Actuators ◽  
Hammerstein Model ◽  
Order Model ◽  
Integer Order ◽  
Rate Dependent ◽  
Rate Correlation

Piezoelectric actuators (PEAs), as a smart material with excellent characteristics, are increasingly used in high-precision and high-speed nano-positioning systems. Different from the usual positioning control or fixed frequency tracking control, the more accurate rate-dependent PEA nonlinear model is needed in random signal dynamic tracking control systems such as active vibration control. In response to this problem, this paper proposes a Hammerstein model based on fractional order rate correlation. The improved Bouc-Wen model is used to describe the asymmetric hysteresis characteristics of PEA, and the fractional order model is used to describe the dynamic characteristics of PEA. The nonlinear rate-dependent hysteresis model can be used to accurately describe the dynamic characteristics of PEA. Compared with the integer order model or linear autoregressive model to describe the dynamic characteristics of the PEA Hammerstein model, the modeling accuracy is higher. Moreover, an artificial bee colony algorithm (DE-ABC) based on differential evolution was proposed to identify model parameters. By adding the mutation strategy and chaos search of the genetic algorithm into the previous ABC, the convergence speed of the algorithm is faster and the identification accuracy is higher, and the simultaneous identification of order and coefficient of the fractional model is realized. Finally, by comparing the simulation and experimental data of multiple sets of sinusoidal excitation with different frequencies, the effectiveness of the proposed modeling method and the accuracy and rapidity of the identification algorithm are verified. The results show that, in the wide frequency range of 1–100 Hz, the proposed method can obtain more accurate rate-correlation models than the Bouc-Wen model, the Hammerstein model based on integer order or the linear autoregressive model to describe dynamic characteristics. The maximum error (Max error) is 0.0915 μm, and the maximum mean square error (RMSE) is 0.0244.

Modeling the Finite Deformation Anisotropic Viscoelastic Behavior of the Cornea

2008 ◽  
Author(s):  
Thao D. Nguyen ◽  
Reese E. Jones ◽  
Brad L. Boyce
Keyword(s):  
Stress Response ◽  
Finite Deformation ◽  
Viscoelastic Properties ◽  
Viscoelastic Behavior ◽  
Element Model ◽  
Image Correlation ◽  
Uniaxial Tensile ◽  
Model Parameters ◽  
Human Cornea ◽  
Viscoelastic Parameters

This paper presents the development of a finite element model for the cornea as a first step towards a physiologically based model to study the role of cornea and sclera biomechanics in glaucoma. We developed a finite-deformation anisotropic constitutive model of the cornea that considers the effects of the fibrilar microstructure on the viscoelastic stress response. The model was base on the hypothesis that the dominant mechanism for the tensile viscoelastic behavior of the cornea is the viscoelastic stretching of the collagen lamellae. This approach yielded two main results. First, the viscoelastic properties of the cornea are derivable directly from the viscoelastic properties of the collagen fibrils and proteoglycan matrix. Second, the anisotropy in the stress response and creep response are determined solely by the arrangement collagen lamellae, which depends on orientation and material position. This allows the model parameters that determines anisotropy to be obtained from microstructural characterizations, such as the X-ray diffraction experiments of Meek and coworkers [1], while the model parameters that determines viscoelasticity to be determined from mechanical experiments. For this initial work, the viscoelastic parameters were fitted to the uniaxial tensile strip tests [2] and inflation tests with digital image correlation (DIC) [3] of bovine cornea performed by our group. Since microstructural characterizations are not available for bovine cornea, we used the data of Aghamohammadzadeh et. al. [1] for the human cornea.

A Comparison Between Fractional-Order and Integer-Order Differential Finite Deformation Viscoelastic Models: Effects of Filler Content and Loading Rate on Material Parameters

2018 ◽  
Vol 10 (09) ◽  
pp. 1850099 ◽  
Author(s):  
Hesam Khajehsaeid
Keyword(s):  
Fractional Order ◽  
Differential Operators ◽  
Filler Content ◽  
Viscoelastic Model ◽  
Constitutive Models ◽  
Viscoelastic Behavior ◽  
Fractional Model ◽  
Material Parameters ◽  
Integer Order ◽  
Viscoelastic Models

Elastomers or rubber-like materials exhibit nonlinear viscoelastic behavior such as creep and relaxation upon mechanical loading. Differential constitutive models and hereditary integrals are the main frameworks followed in the literature for modeling the viscoelastic behavior at finite deformations. Regular differential operators can be replaced by fractional-order derivatives in the standard models in order to make fractional viscoelastic models. In the present paper, the relaxation behavior of elastomers is formulated both in terms of ordinary (integer-order) and fractional differential viscoelastic models. The derived constitutive equations are fitted to several experimental data to compare their efficiency in modeling the stress relaxation phenomenon. Specifically, a fractional viscoelastic model with one fractional dashpot (FD) is compared with two ordinary models including respectively one and two ordinary dashpots (OD). The models are compared in fitting accuracy, number of required material parameters and also variation of parameters from one compound to another to clarify the effects of filler content and deformation rate. It is shown that, the results of the ordinary model with one OD is not good at all. The fractional model with one FD and the ordinary model with two ODs provide good fittings for all compounds whereas the former uses only three parameters and the latter uses five material parameters. For the fractional model, the order of the Maxwell element and the associated relaxation time approximately remain the same for different compounds of each material at certain loading rates, but it is not the case for the ordinary differential models.

scholarly journals Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Fractional Order ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Superior Performance ◽  
Image Description ◽  
Orthogonal Moments ◽  
Integer Order ◽  
Geometric Invariance ◽  
Order Continuous

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

Exploiting Fractional Order PID Controller Methods in Improving the Performance of Integer Order PID Controllers: A GA Based Approach

2009 ◽  
Author(s):  
Bijoy K. Mukherjee ◽  
Santanu Metia ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
Hideki Katagiri ◽  
...  
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Pid Controllers ◽  
Integer Order ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller

The multi-model approach for fractional-order systems modelling

2016 ◽  
Vol 40 (1) ◽  
pp. 331-340 ◽  
Author(s):  
Samia Talmoudi ◽  
Moufida Lahmari
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Global Model ◽  
Fractional Order Systems ◽  
New Approach ◽  
Physical Systems ◽  
Integer Order ◽  
Systems Modelling ◽  
Model Approach

Currently, fractional-order systems are attracting the attention of many researchers because they present a better representation of many physical systems in several areas, compared with integer-order models. This article contains two main contributions. In the first one, we suggest a new approach to fractional-order systems modelling. This model is represented by an explicit transfer function based on the multi-model approach. In the second contribution, a new method of computation of the validity of library models, according to the frequency [Formula: see text], is exposed. Finally, a global model is obtained by fusion of library models weighted by their respective validities. Illustrative examples are presented to show the advantages and the quality of the proposed strategy.

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