A Nonlinear Rubber Material Model Combining Fractional Order Viscoelasticity and Amplitude Dependent Effects

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
N. Gil-Negrete ◽  
J. Vinolas ◽  
L. Kari
Keyword(s):  
Fractional Derivative ◽  
Dynamic Behavior ◽  
Fractional Order ◽  
Constitutive Models ◽  
Material Model ◽  
General Purpose ◽  
Fe Model ◽  
Rubber Material ◽  
Rubber Compounds ◽  
Von Mises

A nonlinear rubber material model is presented, where influences of frequency and dynamic amplitude are taken into account through fractional order viscoelasticity and plasticity, respectively. The problem of simultaneously modeling elastic, viscoelastic, and friction contributions is removed by additively splitting them. Due to the fractional order representation mainly, the number of parameters of the model remains low, rendering an easy fitting of the values from tests on material samples. The proposed model is implemented in a general-purpose finite element (FE) code. Since commercial FE codes do not contain any suitable constitutive model that represents the full dynamic behavior of rubber compounds (including frequency and amplitude dependent effects), a simple approach is used based on the idea of adding stress contributions from simple constitutive models: a mesh overlay technique, whose basic idea is to create a different FE model for each material definition (fractional derivative viscoelastic and elastoplastic), all with identical meshes but with different material definition, and sharing the same nodes. Fractional-derivative viscoelasticity is implemented through user routines and the algorithm for that purpose is described, while available von Mises’ elastoplastic models are adopted to take rate-independent effects into account. Satisfactory results are obtained when comparing the model results with tests carried out in two rubber bushings at a frequency range up to 500 Hz, showing the ability of the material model to accurately describe the complex dynamic behavior of carbon-black filled rubber compounds.

Application of a Smooth Approximation of the Schmid’s Law to a Single Crystal Gas Turbine Blade: Part 1—Theory and Governing Equations

2012 ◽  
Author(s):  
Alessandro D. Ramaglia
Keyword(s):  
Single Crystal ◽  
Constitutive Models ◽  
Material Model ◽  
Research Literature ◽  
Elastic Behaviour ◽  
Full Potential ◽  
Smooth Approximation ◽  
Suitable Material ◽  
Von Mises ◽  
Term Creep

In industrial practice, the choice of the most suitable material model does not solely rely on the ability of the model in describing the intended phenomena. Most of the choice is often based on a trade-off between a great variety of factors. Robustness, cost and time for the minimum testing campaign necessary to identify the model and pre-existing standard practices are only a few of them. This is particularly true in the case of nonlinear structural analyses because of their intrinsic difficulties and the higher level of skills needed to carefully exploit their full potential. So, despite the great progress in this field, in certain cases it is desirable to use plasticity models that are rate-independent and possess very simple hardening terms. This is for example the case in which long term creep can be an issue or when the designer may want to treat separately different phenomena contributing to inelastic deformation. If the material to be modelled is isotropic, commercial FE packages are able to deal with such problems in almost every case. On the contrary for anisotropic materials like Ni-based super-alloys cast as single crystals, the choice of the designer is more limited and despite the large amount of research literature on the subject, single crystal constitutive models remain quite difficult to handle, to implement into FE codes, to calibrate and to validate. Such difficulties, coupled with the unavoidable approximations introduced by any model, often force the practice of using oversimplifications of the material behaviour. In what follows this problem is addressed by showing how single crystal plasticity modelling can be reduced to the adoption of an anisotropic elastic behaviour with a sort of von Mises yield surface.

Development of Noninteraction Material Models With Cyclic Hardening

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Thomas Bouchenot ◽  
Bassem Felemban ◽  
Cristian Mejia ◽  
Ali P. Gordon
Keyword(s):  
Elevated Temperatures ◽  
Kinematic Hardening ◽  
Critical Role ◽  
Constitutive Models ◽  
Cyclic Hardening ◽  
Material Model ◽  
General Purpose ◽  
Pressure Vessels ◽  
Single Element ◽  
Critical Components

Simulation plays a critical role in the development and evaluation of critical components that are regularly subjected to mechanical loads at elevated temperatures. The cost, applicability, and accuracy of either numerical or analytical simulations are largely dependent on the material model chosen for the application. A noninteraction (NI) model derived from individual elastic, plastic, and creep components is developed in this study. The candidate material under examination for this application is 2.25Cr–1Mo, a low-alloy ferritic steel commonly used in chemical processing, nuclear reactors, pressure vessels, and power generation. Data acquired from prior research over a range of temperatures up to 650 °C are used to calibrate the creep and plastic components described using constitutive models generally native to general-purpose fea. Traditional methods invoked to generate constitutive modeling coefficients employ numerical fittings of hysteresis data, which result in values that are neither repeatable nor display reasonable temperature dependence. By extrapolating simplifications commonly used for reduced-order model approximations, an extension utilizing only the cyclic Ramberg–Osgood (RO) coefficients has been developed. This method is used to identify the nonlinear kinematic hardening (NLKH) constants needed at each temperature. Single-element simulations are conducted to verify the accuracy of the approach. Results are compared with isothermal and nonisothermal literature data.

Application of Ramberg-Osgood Plasticity to Determine Cyclic Hardening Parameters

2016 ◽  
Author(s):  
Thomas Bouchenot ◽  
Bassem Felemban ◽  
Cristian Mejia ◽  
Ali P. Gordon
Keyword(s):  
Elevated Temperatures ◽  
Kinematic Hardening ◽  
Constitutive Models ◽  
Cyclic Hardening ◽  
Material Model ◽  
General Purpose ◽  
Pressure Vessels ◽  
Component Level ◽  
Critical Components ◽  
Plastic Components

Critical components of modern turbomachinery are frequently subjected to a myriad of service conditions that include diverse mechanical loads at elevated temperatures. The cost, applicability, and accuracy of either numerical or analytical component-level simulations are largely dependent on the material model chosen for the application. A non-interaction (NI) model derived from individual elastic, plastic, and creep components is developed in this study. The candidate material under examination for this application is 2.25Cr-1Mo, a low-alloy ferritic steel commonly used in chemical processing, nuclear reactors, pressure vessels, and power generation. Data acquired from literature over a range of temperatures up to 650°C are used to calibrate the creep and plastic components described using constitutive models generally native to general-purpose FEA. Traditional methods invoked to generate coefficients for advanced constitutive models such as non-linear kinematic hardening employ numerical fittings of hysteresis data, which result in values that are neither repeatable nor display reasonable temperature-dependence. By extrapolating simplifications commonly used for reduced-order model approximations, an extension utilizing only the cyclic Ramberg-Osgood coefficients has been developed to identify these parameters. Unit cell simulations are conducted to verify the accuracy of the approach. Results are compared with isothermal and non-isothermal literature data.

Finite Element Modeling of Aortic Tissue Using High Speed Experimental Data

2005 ◽  
Author(s):  
Muralikrishna Maddali ◽  
Chirag S. Shah ◽  
King H. Yang
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
High Speed ◽  
Material Model ◽  
Traumatic Rupture ◽  
Aortic Tissue ◽  
Model Parameters ◽  
Fe Model ◽  
Rubber Material ◽  
Material Constants

Traumatic rupture of the aorta (TRA) is responsible for 10% to 20% of motor vehicle fatalities [1]. Both finite element (FE) modeling and experimental investigations have enhanced our understanding of the injury mechanisms associated with TRA. Because accurate material properties are essential for the development of correct and authoritative FE model predictions, the objective of the current study was to identify a suitable material model and model parameters for aorta tissue that can be incorporated into FE aorta models for studying TRA. An Ogden rubber material (Type 77B in LS-DYNA 970) was used to simulate a series of high speed uniaxial experiments reported by Mohan [2] using a dumbbell shaped FE model representing human aortic tissue. Material constants were obtained by fitting model simulation results against experimentally obtained corridors. The sensitivity of the Ogden rubber material model was examined by altering constants G and alpha (α) and monitoring model behavior. One single set of material constants (α = 25.3, G = 0.02 GPa, and μ = 0.6000E-06 GPa) was found to fit uniaxial data at strain rates of approximately 100 s−1 for both younger and older aortic tissue specimens. Until a better material model is derived and other experimental data are obtained, it is recommended that the Ogden material model and associated constants derived from the current study be used to represent aorta tissue properties when using FE methods to investigate mechanisms of TRA.

Application of a Smooth Approximation of the Schmid's Law to a Single Crystal Gas Turbine Blade

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Alessandro D. Ramaglia
Keyword(s):  
Single Crystal ◽  
Constitutive Models ◽  
Material Model ◽  
Research Literature ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Full Potential ◽  
Smooth Approximation ◽  
Suitable Material ◽  
Von Mises

In industrial practice the choice of the most suitable material model does not solely rely on the ability of the model in describing the intended phenomena. Most of the choice is often based on a trade-off between a great variety of factors. Robustness, cost, and time for the minimum testing campaign necessary to identify the model and preexisting standard practices are only a few of them. This is particularly true in the case of nonlinear structural analyses because of their intrinsic difficulties and the higher level of skills needed to carefully exploit their full potential. So, despite the great progress in this field, in certain cases it is desirable to use plasticity models that are rate independent and possess very simple hardening terms. This is for example the case in which long term creep can be an issue or when the designer may want to treat separately different phenomena contributing to inelastic deformation. If the material to be modeled is isotropic, commercial finite element (FE) packages are able to deal with such problems in almost every case. On the contrary for anisotropic materials like Ni-based superalloys cast as single crystals, the choice of the designer is more limited and despite the large amount of research literature on the subject, single crystal constitutive models remain quite difficult to handle, to implement into FE codes, to calibrate, and to validate. Such difficulties, coupled with the unavoidable approximations introduced by any model, often force the practice of using oversimplifications of the material behavior. In what follows this problem is addressed by showing how single crystal plasticity modeling can be reduced to the adoption of an anisotropic elastic behavior with a sort of von Mises yield surface.

Stress Field Around a Large Opening in a Pressure Vessel During a Major Repair

2009 ◽  
Author(s):  
Erik Garrido ◽  
Euro Casanova
Keyword(s):  
Pressure Vessel ◽  
New Technologies ◽  
Mechanical Design ◽  
General Purpose ◽  
Pressure Vessels ◽  
Mechanical Equipment ◽  
Stress Distributions ◽  
Large Opening ◽  
Von Mises ◽  
Case Basis

It is a regular practice in the oil industry to modify mechanical equipment to incorporate new technologies and to optimize production. In the case of pressure vessels, it is occasionally required to cut large openings in their walls in order to have access to the interior part of the equipment for executing modifications. This cutting process produces temporary loads, which were obviously not considered in the original mechanical design. Up to now, there is not a general purpose specification for approaching the assessments of stress levels once a large opening in a vertical pressure vessel has been made. Therefore stress distributions around large openings are analyzed on a case-by-case basis without a reference scheme. This work studies the distribution of the von Mises equivalent stresses around a large opening in FCC Regenerators during internal cyclone replacement, which is a frequently required practice for this kind of equipment. A finite element parametric model was developed in ANSYS, and both numerical results and illustrating figures are presented.

scholarly journals Fractional-Order Colour Image Processing

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 457
Author(s):  
Manuel Henriques ◽  
Duarte Valério ◽  
Paulo Gordo ◽  
Rui Melicio
Keyword(s):  
Image Processing ◽  
Edge Detection ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Grey Scale ◽  
Colour Image ◽  
Colour Image Processing ◽  
Image Processing Algorithms ◽  
Processing Algorithms

Many image processing algorithms make use of derivatives. In such cases, fractional derivatives allow an extra degree of freedom, which can be used to obtain better results in applications such as edge detection. Published literature concentrates on grey-scale images; in this paper, algorithms of six fractional detectors for colour images are implemented, and their performance is illustrated. The algorithms are: Canny, Sobel, Roberts, Laplacian of Gaussian, CRONE, and fractional derivative.

scholarly journals Variable-Order Fractional Models for Wall-Bounded Turbulent Flows

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 782
Author(s):  
Fangying Song ◽  
George Em Karniadakis
Keyword(s):  
Fractional Derivative ◽  
Turbulent Flows ◽  
Fractional Order ◽  
Variable Order ◽  
Universal Curve ◽  
Reynolds Stresses ◽  
Continuous Change ◽  
Mean Velocity ◽  
Symmetric Variable ◽  
Fractional Models

Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with relatively slow progress in the last few decades beyond the log law, which only describes the intermediate region in wall-bounded turbulence, i.e., 30–50 y+ to 0.1–0.2 R+ in a pipe of radius R. Here, we propose a fundamentally new approach based on fractional calculus to model the entire mean velocity profile from the wall to the centerline of the pipe. Specifically, we represent the Reynolds stresses with a non-local fractional derivative of variable-order that decays with the distance from the wall. Surprisingly, we find that this variable fractional order has a universal form for all Reynolds numbers and for three different flow types, i.e., channel flow, Couette flow, and pipe flow. We first use existing databases from direct numerical simulations (DNSs) to lean the variable-order function and subsequently we test it against other DNS data and experimental measurements, including the Princeton superpipe experiments. Taken together, our findings reveal the continuous change in rate of turbulent diffusion from the wall as well as the strong nonlocality of turbulent interactions that intensify away from the wall. Moreover, we propose alternative formulations, including a divergence variable fractional (two-sided) model for turbulent flows. The total shear stress is represented by a two-sided symmetric variable fractional derivative. The numerical results show that this formulation can lead to smooth fractional-order profiles in the whole domain. This new model improves the one-sided model, which is considered in the half domain (wall to centerline) only. We use a finite difference method for solving the inverse problem, but we also introduce the fractional physics-informed neural network (fPINN) for solving the inverse and forward problems much more efficiently. In addition to the aforementioned fully-developed flows, we model turbulent boundary layers and discuss how the streamwise variation affects the universal curve.

scholarly journals Vibration Equation of Fractional Order Describing Viscoelasticity and Viscous Inertia

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 850-856 ◽  
Author(s):  
Jun-Sheng Duan ◽  
Yun-Yun Xu
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Steady State Response ◽  
Vibration System ◽  
Derivative Operator ◽  
Vibration Equation ◽  
State Response ◽  
Frequency Relation

Abstract The steady state response of a fractional order vibration system subject to harmonic excitation was studied by using the fractional derivative operator ${}_{-\infty} D_t^\beta,$where the order β is a real number satisfying 0 ≤ β ≤ 2. We derived that the fractional derivative contributes to the viscoelasticity if 0 < β < 1, while it contributes to the viscous inertia if 1 < β < 2. Thus the fractional derivative can represent the “spring-pot” element and also the “inerterpot” element proposed in the present article. The viscosity contribution coefficient, elasticity contribution coefficient, inertia contribution coefficient, amplitude-frequency relation, phase-frequency relation, and influence of the order are discussed in detail. The results show that fractional derivatives are applicable for characterizing the viscoelasticity and viscous inertia of materials.

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