Optimization of a Viscoelastic Structure: The Seat-Belt Problem

1969 ◽  
Vol 36 (3) ◽  
pp. 565-572 ◽  
Author(s):  
W. Nachbar ◽  
J. B. Schipmo¨lder
Keyword(s):  
Seat Belt ◽  
Viscoelastic Model ◽  
Small Strain ◽  
The Body ◽  
Strain Rates ◽  
Maximum Displacement ◽  
Critical Displacement ◽  
Viscoelastic Models ◽  
Maximum Value ◽  
Linear Viscoelastic

Optimization of the parameters of elementary linear viscoelastic models is considered for the design of a lap seat belt in automobiles. The vehicle is assumed to stop abruptly on impact. The parameters are optimized to allow the speed of the vehicle before impact to have the largest permissible value consistent with constraints imposed for the safety of the user of the belt. The constraints chosen here are: (a) the maximum displacement of the body after impact is equal to or less than a prescribed critical displacement; (b) the forward speed of the body at the critical displacement does not exceed a prescribed maximum value; (c) the force exerted by the belt on the body during the motion following impact does not exceed a prescribed maximum value. It is found that the optimized Kelvin-Voigt viscoelastic model is nearly 40 percent more effective than the purely elastic material. It is nearly as effective as constant deceleration. An additional and advantageous property is proposed, moreover, for belts of viscoelastic materials. This is that the material should have a relatively low spring rate at relatively small strain rates. The optimized belts for the elementary viscoelastic models are shown to be quite stiff at low strain rates, however.

Viscoelastic Properties of Aorta From Oscillatory Pressure Tests

2011 ◽  
Author(s):  
Vasily Romanov ◽  
Mobin Rastgar Agah ◽  
Kurosh Darvish
Keyword(s):  
Blood Vessels ◽  
Material Properties ◽  
Large Deformations ◽  
Aortic Rupture ◽  
Viscoelastic Model ◽  
The Body ◽  
Time Dependency ◽  
Linear Viscoelastic ◽  
Almost All ◽  
The Relationship

Aorta is the largest and most important artery in the body due to its role in conveying all of the oxygenated blood to smaller branches and ultimately to all of the organs in the body. Knowing its mechanical characteristics and material properties is a basic stage in almost all studies on aorta e.g. evaluating the effect of aging and disease, design and manufacturing of compatible stents and traumatic aortic rupture. Since blood vessels are non-homogeneous, non-linear viscoelastic materials and can experience large deformations, a unique formulation that can describe their mechanical behavior under various loading conditions has not been developed yet. Several previous studies looked into modeling of the blood vessels at large deformation, but the models developed did not include the time dependency of the material [1,2]. In this work, we characterized the material properties of aorta under biaxial oscillatory loading at large deformations taking into account its time dependency. A viscoelastic model was developed to describe the relationship between the inflation and pressure.

On the Development of Creep Laws for Rubber in the Parallel Rheological Framework

2019 ◽  
Vol 47 (1) ◽  
pp. 2-30 ◽  
Author(s):  
Gautam Sagar ◽  
Dong Zheng ◽  
Anuwat Suwannachit ◽  
Maik Brinkmeier ◽  
Kristin Fietz ◽  
...  
Keyword(s):  
Complex Modulus ◽  
Dynamic Stiffness ◽  
Viscoelastic Model ◽  
American Chemical Society ◽  
Small Strain ◽  
Chemical Society ◽  
Material Behavior ◽  
Constitutive Law ◽  
Rate Dependency ◽  
Linear Viscoelastic

ABSTRACT It is widely known that filler-reinforced rubber material in tires shows a very complicated material behavior when subjected to cyclic loadings. One of the most interesting effects for rolling tires is the nonlinear rate-dependent behavior, which is implicitly linked to the amplitude dependency of dynamic stiffness (Payne effect) at a given frequency and temperature. This effect, however, cannot be described by a conventional linear viscoelastic constitutive law, e.g., the Prony series model. Several nonlinear viscoelastic material models have been proposed in the last decades. Among others, Lapczyk et al. (Lapczyk, I., Hurtado, J. A., and Govindarajan, S. M., “A Parallel Rheological Framework for Modeling Elastomers and Polymers,” 182nd Technical Meeting of the Rubber Division of the American Chemical Society, Cincinnati, Ohio, October 2012) recently proposed a quite general framework for the class of nonlinear viscoelasticity, called parallel rheological framework (PRF), which is followed by Abaqus. The model has an open option for different types of viscoelastic creep laws. In spite of the very attractive nonlinear rate-dependency, the identification of material parameters becomes a very challenging task, especially when a wide frequency and amplitude range is of interest. This contribution points out that the creep law is numerically sound if it can be degenerated to the linear viscoelastic model at a very small strain amplitude, which also significantly simplifies model calibration. More precisely, the ratio between viscoelastic stress and strain rate has to converge to a certain value, i.e., the viscosity in a linear viscoelastic case. The creep laws implemented in Abaqus are discussed in detail here, with a focus on their fitting capability. The conclusion of the investigation consequently gives us a guideline to develop a new creep law in PRF. Here, one creep law from Abaqus that meets the requirements of our guideline has been selected. A fairly good fit of the model is shown by the comparison of the simulated complex modulus in a wide frequency and amplitude range with experimental results.

A Nonlinear Viscoelastic Model for the Relaxation Behavior of Tendon

2012 ◽  
Author(s):  
Frances M. Davis ◽  
Raffaella De Vita
Keyword(s):  
Stress Relaxation ◽  
Relaxation Function ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Relaxation Behavior ◽  
Successful Model ◽  
Viscoelastic Models ◽  
Nonlinear Viscoelastic ◽  
Linear Viscoelastic ◽  
Nonlinear Viscoelastic Model

Tendons are viscoelastic materials which undergo stress relaxation when held at a constant strain. The most successful model used to describe the viscoelastic behavior of tendons is the quasi-linear viscoelastic (QLV) model [1]. In the QLV model, the relaxation function is assumed to be a separable function of time and strain. Recently, this assumption has been shown to be invalid for tendons [2] thus suggesting the need for new nonlinear viscoelastic models.

scholarly journals Nonrigid Registration of Monomodal MRI Using Linear Viscoelastic Model

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Jian Yang ◽  
Yang Chen ◽  
Jingfan Fan ◽  
Songyuan Tang
Keyword(s):  
Fluid Model ◽  
Viscoelastic Model ◽  
Elastic Solid ◽  
Maxwell Model ◽  
Nonrigid Registration ◽  
Registration Accuracy ◽  
Maximum Displacement ◽  
Linear Viscoelastic ◽  
Synthetic Datasets ◽  
Linear Viscoelastic Model

This paper describes a method for nonrigid registration of monomodal MRI based on physical laws. The proposed method assumes that the properties of image deformations are like those of viscoelastic matter, which exhibits the properties of both an elastic solid and a viscous fluid. Therefore, the deformation fields of the deformed image are constrained by both sets of properties. After global registration, the local shape variations are assumed to have the properties of the Maxwell model of linear viscoelasticity, and the deformation fields are constrained by the corresponding partial differential equations. To speed up the registration, an adaptive force is introduced according to the maximum displacement of each iteration. Both synthetic datasets and real datasets are used to evaluate the proposed method. We compare the results of the linear viscoelastic model with those of the fluid model on the basis of both the standard and adaptive forces. The results demonstrate that the adaptive force increases in both models and that the linear viscoelastic model improves the registration accuracy.

Free volume based nonlinear viscoelastic model for polyurea over a wide range of strain rates and temperatures

2021 ◽  
Vol 152 ◽  
pp. 103650
Author(s):  
Chencheng Gong ◽  
Yan Chen ◽  
Ting Li ◽  
Zhanli Liu ◽  
Zhuo Zhuang ◽  
...  
Keyword(s):  
Free Volume ◽  
Viscoelastic Model ◽  
Strain Rates ◽  
Nonlinear Viscoelastic ◽  
Wide Range ◽  
Nonlinear Viscoelastic Model

Identification of Nonlinear Viscoelastic Models of Flexible Polyurethane Foam From Uniaxial Compression Data

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Yousof Azizi ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Uniaxial Compression ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Nonlinear Viscoelastic ◽  
Compression Data ◽  
Computationally Intensive ◽  
Nonlinear Viscoelastic Model ◽  
Flexible Polyurethane

Flexible polyethylene foam is used in many engineering applications. It exhibits nonlinear and viscoelastic behavior which makes it difficult to model. To date, several models have been developed to characterize the complex behavior of foams. These attempts include the computationally intensive microstructural models to continuum models that capture the macroscale behavior of the foam materials. In this research, a nonlinear viscoelastic model, which is an extension to previously developed models, is proposed and its ability to capture foam response in uniaxial compression is investigated. It is hypothesized that total stress can be decomposed into the sum of a nonlinear elastic component, modeled by a higher-order polynomial, and a nonlinear hereditary type viscoelastic component. System identification procedures were developed to estimate the model parameters using uniaxial cyclic compression data from experiments conducted at six different rates. The estimated model parameters for individual tests were used to develop a model with parameters that are a function of strain rates. The parameter estimation technique was modified to also develop a comprehensive model which captures the uniaxial behavior of all six tests. The performance of this model was compared to that of other nonlinear viscoelastic models.

Application of a Viscoelastic Model for Polyester Mooring

2010 ◽  
Author(s):  
J. W. Kim ◽  
J. H. Kyoung ◽  
A. Sablok
Keyword(s):  
Material Properties ◽  
Viscoelastic Model ◽  
Practical Method ◽  
Time Dependent ◽  
Mooring Line ◽  
New Model ◽  
Global Performance ◽  
Excitation Period ◽  
Linear Viscoelastic ◽  
Floating Platforms

A new practical method to simulate time-dependent material properties of polyester mooring line is proposed. The time-dependent material properties of polyester rope are modeled with a standard linear solid (SLS) model, which is one of the simplest forms of a linear viscoelastic model. The viscoelastic model simulates most of the mechanical properties of polyester rope such as creep, strain-stress hysteresis and excitation period-dependent stiffness. The strain rate-stress relation of the SLS model has been re-formulated to a stretch-tension relation, which is more suitable for implementation into global performance and mooring analyses tools for floating platforms. The new model has been implemented to a time-domain global performance analysis software and applied to simulate motion of a spar platform with chain-polyester-chain mooring system. The new model provides accurate platform offset without any approximation on the mean environmental load and can simulate the transient effect due to the loss of a mooring line during storm conditions, which has not been possible to simulate using existing dual-stiffness models.

A non-linear viscoelastic model with structure-dependent relaxation times

1976 ◽  
Vol 1 (2) ◽  
pp. 147-157 ◽  
Author(s):  
D. Acierno ◽  
F.P. La Mantia ◽  
G. Marrucci ◽  
G. Rizzo ◽  
G. Titomanlio
Keyword(s):  
Relaxation Times ◽  
Viscoelastic Model ◽  
Non Linear ◽  
Linear Viscoelastic ◽  
Linear Viscoelastic Model

STRESS RELAXATION OF MAGNETORHEOLOGICAL FLUIDS

2002 ◽  
Vol 16 (17n18) ◽  
pp. 2655-2661
Author(s):  
W. H. LI ◽  
G. CHEN ◽  
S. H. YEO ◽  
H. DU
Keyword(s):  
Stress Relaxation ◽  
Viscoelastic Model ◽  
Relaxation Modulus ◽  
Damping Function ◽  
Mr Fluids ◽  
Large Step ◽  
Linear Viscoelastic ◽  
Predicted Values ◽  
Two Parameters ◽  
Step Strain

In this paper, the experimental and modeling study and analysis of the stress relaxation characteristics of magnetorheological (MR) fluids under step shear are presented. The experiments are carried out using a rheometer with parallel-plate geometry. The applied strain varies from 0.01% to 100%, covering both the pre-yield and post-yield regimes. The effects of step strain, field strength, and temperature on the stress modulus are addressed. For small step strain ranges, the stress relaxation modulus G(t,γ) is independent of step strain, where MR fluids behave as linear viscoelastic solids. For large step strain ranges, the stress relaxation modulus decreases gradually with increasing step strain. Morever, the stress relaxation modulus G(t,γ) was found to obey time-strain factorability. That is, G(t,γ) can be represented as the product of a linear stress relaxation G(t) and a strain-dependent damping function h(γ). The linear stress relaxation modulus is represented as a three-parameter solid viscoelastic model, and the damping function h(γ) has a sigmoidal form with two parameters. The comparison between the experimental results and the model-predicted values indicates that this model can accurately describe the relaxation behavior of MR fluids under step strains.

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