An Orthotropic Viscoelastic Winding Model Including a Nonlinear Radial Stiffness

1997 ◽  
Vol 64 (1) ◽  
pp. 201-208 ◽  
Author(s):  
W. R. Qualls ◽  
J. K. Good
Keyword(s):  
Numerical Solutions ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Maxwell Model ◽  
Stress Distributions ◽  
Convolution Integral ◽  
Integral Boundary ◽  
Transient Stress ◽  
Radial Stiffness ◽  
Generalized Maxwell Model

A realistic and adaptive viscoelastic model for prediction of transient wound roll stress distributions is presented. The web material is taken to be orthotropic with a nonlinear radial stiffness dependent upon interlayer pressure. Viscoelastic behavior is represented by a generalized Maxwell model for creep written as a convolution integral. Numerical solutions to the resulting integral boundary value problem give both initial and transient stress distributions within the wound roll. The model is successfully compared to the analytical solution for a simple case of isotropy as well as to published works on this topic. In contrasting the solutions, the advantages and adaptability of this formulation will be readily seen.

Viscoelastic Damping Effect on Brake Squeal Noise

2009 ◽  
Author(s):  
Gael Chevallier ◽  
Franck Renaud ◽  
Jean-Luc Dion
Keyword(s):  
Degrees Of Freedom ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Maxwell Model ◽  
Element Model ◽  
Brake Squeal ◽  
Generalized Maxwell Model ◽  
Space Formulation ◽  
Damping Materials ◽  
Squeal Noise

Brake squeal remains a widespread cause for discomfort in automobiles. Manufacturers overcome this problem by adding damping materials in their systems. The purpose of this work is to take into account the damping in the modeling. As the materials exhibit a viscoelastic behavior, the authors chose to model the damping with the Generalized Maxwell model. Moreover, the authors have tested their method on a detailed Finite Element-model of a brake system. To compute the complex poles of the model, the authors have established a state-space formulation of the viscoelastic model with a new assumption that allows one to reduce the number of states. Making the computation on the whole model is rather difficult due to the number of Degrees Of Freedom, the model is thus reduced on a basis constituted with the eigenvectors of the undamped model. Several results are also presented and discussed as the observed phenomena are rather different from the results obtained with undamped systems.

Linking Internal Dissipation Mechanisms to the Effective Complex Viscoelastic Moduli of Ferroelectrics

2016 ◽  
Vol 84 (2) ◽  
Author(s):  
Charles S. Wojnar ◽  
Dennis M. Kochmann
Keyword(s):  
Microstructure Evolution ◽  
Domain Switching ◽  
Constitutive Models ◽  
Viscoelastic Behavior ◽  
Maxwell Model ◽  
Hysteretic Behavior ◽  
Ferroelectric Ceramics ◽  
Internal Variables ◽  
Viscoelastic Parameters ◽  
Generalized Maxwell Model

Microstructural mechanisms such as domain switching in ferroelectric ceramics dissipate energy, the nature, and extent of which are of significant interest for two reasons. First, dissipative internal processes lead to hysteretic behavior at the macroscale (e.g., the hysteresis of polarization versus electric field in ferroelectrics). Second, mechanisms of internal friction determine the viscoelastic behavior of the material under small-amplitude vibrations. Although experimental techniques and constitutive models exist for both phenomena, there is a strong disconnect and, in particular, no advantageous strategy to link both for improved physics-based kinetic models for multifunctional rheological materials. Here, we present a theoretical approach that relates inelastic constitutive models to frequency-dependent viscoelastic parameters by linearizing the kinetic relations for the internal variables. This enables us to gain qualitative and quantitative experimental validation of the kinetics of internal processes for both quasistatic microstructure evolution and high-frequency damping. We first present the simple example of the generalized Maxwell model and then proceed to the case of ferroelectric ceramics for which we predict the viscoelastic response during domain switching and compare to experimental data. This strategy identifies the relations between microstructural kinetics and viscoelastic properties. The approach is general in that it can be applied to other rheological materials with microstructure evolution.

scholarly journals Investigation on viscoelastic behavior of virgin EPDM/ reclaimed rubber blends using Generalized Maxwell Model (GMM)

2021 ◽  
Vol 93 ◽  
pp. 106989
Author(s):  
Atefeh Salimi ◽  
Foroud Abbassi-Sourki ◽  
Mohammad Karrabi ◽  
Mir Hamid Reza Ghoreishy
Keyword(s):  
Viscoelastic Behavior ◽  
Maxwell Model ◽  
Rubber Blends ◽  
Generalized Maxwell Model

Nonlinear Dynamic Viscoelastic Model for Osteoarthritic Cartilage Indentation Force

2011 ◽  
Author(s):  
A. Vidal-Lesso ◽  
E. Ledesma-Orozco ◽  
R. Lesso-Arroyo ◽  
L. Daza-Benitez
Keyword(s):  
Mechanical Properties ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Indentation Test ◽  
Maxwell Model ◽  
Relaxation Curve ◽  
Geometrical Parameters ◽  
Osteoarthritic Cartilage

Biomechanical properties and dynamic response of soft tissues as articular cartilage remains issues for attention. Currently, linear isotropic models are still used for cartilage analysis in spite of its viscoelastic nature. Therefore, the aim of this study was to propose a nonlinear viscoelastic model for cartilage indentation that combines the geometrical parameters and velocity of the indentation test with the thickness of the sample as well as the mechanical properties of the tissue changing over time due to its viscoelastic behavior. Parameters of the indentation test and mechanical properties as a function of time were performed in Laplace space where the constitutive equation for viscoelasticity and the convolution theorem was applied in addition with the Maxwell model and Hayes et al. model for instantaneous elastic modulus. Results of the models were compared with experimental data of indentation tests on osteoarthritic cartilage of a unicompartmental osteoarthritis cases. The models showed a strong fit for the axial indentation nonlinear force in the loading curve (R2 = 0.992) and a good fit for unloading (R2 = 0.987), while an acceptable fit was observed in the relaxation curve (R2 = 0.967). These models may be used to study the mechanical response of osteoarthritic cartilage to several dynamical and geometrical test conditions.

Experimental Determination of Layer-Specific Hyperelastic Parameters of Human Descending Thoracic Aortas

2019 ◽  
Author(s):  
Isabella Bozzo ◽  
Marco Amabili ◽  
Prabakaran Balasubramanian ◽  
Ivan Breslavsky ◽  
Giovanni Ferrari
Keyword(s):  
Storage Modulus ◽  
Thoracic Aorta ◽  
Loss Tangent ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Axial Direction ◽  
Maxwell Model ◽  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Descending Thoracic Aorta

Abstract Heart disease is the second leading cause of death in Canada resulting in $20.9 billion annual healthcare expenditures [1,2]. Understanding the mechanics of the human descending thoracic aorta is fundamental for comprehending the development of pathologies and improving surgical prostheses. This study presents hyperelastic and viscoelastic material characterizations of the human descending thoracic aorta from twelve different donors, with a mean age of 49.4 years. The specimens were dissected into the three constituent layers: intima, media and adventitia. Evaluating the layer-specific opening angles led to the computation of the circumferential residual stresses. Uniaxial tensile tests of each layer, in both the circumferential and axial direction, were used to model the hyperelastic behavior according to the Gasser-Ogden-Holzapfel model (GOH). The storage modulus and loss tangent for the layers were obtained from uniaxial harmonic excitations at varied frequencies, to model the viscoelastic behavior with the generalized Maxwell model. The results showed a positive correlation between age and stiffness for all layers, both axially and circumferentially. Similar loss tangent values were found across the three layers. A large increase in the storage modulus from static to dynamic experiments further corroborates the importance of a viscoelastic model of the aorta, rather than solely hyperelastic.

scholarly journals A new identification method of viscoelastic behavior: Application to the generalized Maxwell model

2011 ◽  
Vol 25 (3) ◽  
pp. 991-1010 ◽  
Author(s):  
Franck Renaud ◽  
Jean-Luc Dion ◽  
Gaël Chevallier ◽  
Imad Tawfiq ◽  
Rémi Lemaire
Keyword(s):  
Viscoelastic Behavior ◽  
Maxwell Model ◽  
Identification Method ◽  
Generalized Maxwell Model

scholarly journals Maxwell model geotextile encased stone column in soft soil improvement

2021 ◽  
Vol 4 (1) ◽  
pp. first
Author(s):  
Phạm Tiến Bách ◽  
Võ Đại Nhật ◽  
Nguyễn Việt Kỳ ◽  
Lê Quân
Keyword(s):  
Ground Improvement ◽  
Soft Soil ◽  
Great Influence ◽  
Viscoelastic Behavior ◽  
Maxwell Model ◽  
Soil Improvement ◽  
Time Dependent ◽  
Dependent Behavior ◽  
Generalized Maxwell Model ◽  
Matlab Programming

In the field of geotechnical – soft soil improvement, the mathematical model or mechanical model is one of the important input parameters for the design calculations or studies. The determination of the appropriateness of the models has a great influence on the accuracy results of design and calculation as well as the sustainable stability of soft ground after improvement. On the contrary, the selection of inadequate calculation models will lead to increased costs of soft soil improvement, possibly even leading to the destabilization of the work and causing immense loss of people and property. Recently, many projects major highway after construction design in use has not meet the requirements of the standard, leading to wasted money and time of individuals, organizations, and the state of post-treatment. Therefore, the research and application of using mathematical or mechanical models in accordance with the new soft soil improvement method will greatly help as well as add additional options for soft soil improvement in Vietnam. The soft soil deformation is not only related to load but also to load time. The change in stress and deformation of weak soil over time is called rheology, and in this study is the viscoelastic behavior. From the above reasons, we try to apply a generalized Maxwell model to explain the viscoelastic behavior of a soft soil. In particular, the time-dependent behavior of a viscoelastic soft soil was represented by using the Maxwell rheological model. The Matlab programming code helps to solve numerically all the equation of the mathematical exhibition of the generalized Maxwell model results. We acknowledge that the generalized Maxwell model is superior in demonstrating the time-dependent behavior of soft soil. The results probably show that this is one of the effective models to predict the behavior of soft soils in ground improvement with GEC.

scholarly journals A POROUS VISCOELASTIC MODEL FOR THE CELL CYTOSKELETON

2018 ◽  
Vol 59 (4) ◽  
pp. 472-498 ◽  
Author(s):  
CALINA A. COPOS ◽  
ROBERT D. GUY
Keyword(s):  
Immersed Boundary Method ◽  
Cell Biology ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Viscoelastic Model ◽  
Extracellular Fluid ◽  
Microfluidic Channel ◽  
Maxwell Model ◽  
Immersed Boundary ◽  
Boundary Method

The immersed boundary method is a widely used mixed Eulerian/Lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids. In this work, we consider a poroelastic immersed boundary method in which a fluid permeates a porous, elastic structure of negligible volume fraction, and extend this method to include stress relaxation of the material. The porous viscoelastic method presented here is validated for a prescribed oscillatory shear and for an expansion driven by the motion at the boundary of a circular material by comparing numerical solutions to an analytical solution of the Maxwell model for viscoelasticity. Finally, an application of the modelling framework to cell biology is provided: passage of a cell through a microfluidic channel. We demonstrate that the rheology of the cell cytoplasm is important for capturing the transit time through a narrow channel in the presence of a pressure drop in the extracellular fluid.

Generalized Maxwell model for the viscoelastic behavior of a soda-lime-silica glass under low frequency shear loading

1997 ◽  
Vol 36 (2) ◽  
pp. 173-186
Author(s):  
Lucas Duffrène *, † , Ren&#x ◽  
Hélène Burlet ◽  
Roland Piques ◽  
Annelise Faivre ◽  
Anas Sekkat ◽  
...  
Keyword(s):  
Silica Glass ◽  
Low Frequency ◽  
Viscoelastic Behavior ◽  
Maxwell Model ◽  
Soda Lime ◽  
Shear Loading ◽  
Generalized Maxwell Model ◽  
Soda Lime Silica Glass

Predicting Polyurethane Shape Memory Behaviors in Stress-Controlled Situations Using a Viscoelastic Model

2013 ◽  
Vol 575-576 ◽  
pp. 101-106
Author(s):  
Zhao Jing Wang ◽  
Ling Luo ◽  
Yu Xi Jia ◽  
Jun Peng Gao ◽  
Xiao Su Yi
Keyword(s):  
Shape Memory ◽  
Heating Rate ◽  
Smart Materials ◽  
Memory Performance ◽  
Superposition Principle ◽  
Viscoelastic Model ◽  
Maxwell Model ◽  
Generalized Maxwell Model ◽  
Potential Applications ◽  
Time Temperature Superposition Principle

As an outstanding class in smart materials of particular interest, shape memory polymers (SMPs) and their composites are drawing more and more attentions due to their potential applications in fields like biomedical and spacecraft industry. In this paper, shape memory behaviors of polyurethane (PU) in stress-controlled situations are simulated on the basis of the generalized Maxwell model and the time-temperature superposition principle. The free recovery cycles under three different imposed stresses and the influence on shape memory behaviors caused by changing heating rate are discussed. As the results reveal, the generalized Maxwell model can be used to describe the PU shape memory performance, and the shape recovery temperature increases with the increase of heating rate.

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