A New Constitutive Model for the Compressibility of Elastomers at Finite Deformations

2001 ◽  
Vol 74 (4) ◽  
pp. 541-559 ◽  
Author(s):  
Jeffrey E. Bischoff ◽  
Ellen M. Arruda ◽  
Karl Grosh
Keyword(s):  
Uniaxial Tension ◽  
Volume Change ◽  
Constitutive Models ◽  
Hydrostatic Compression ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Compression Tests ◽  
Volume Response ◽  
Using Data ◽  
Nonlinear Elastic

Abstract Although traditional constitutive models for rubbery elastic materials are incompressible, many materials that demonstrate nonlinear elastic behavior are somewhat compressible. Clearly important in hydrostatic deformations, compressibility can also significantly affect the response of elastomers in applications for which several boundaries are rigidly fixed, such as bushings, or triaxial states of stress are realized. Compressibility is also important for convergence of finite element simulations in which a rubbery elastic constitutive law is in use. Volume changes that reflect compressibility have been observed historically in both uniaxial tension and hydrostatic compression tests; however, there appear to be no data obtained from both types of tests on the same material by which to validate a compressible hyperelastic law. In this paper, we propose a new compressible hyperelastic constitutive law for elastomers and other rubbery materials in which entropy and internal energy changes contribute to the volume change. Using data from the literature, we show that this law is capable of reproducing both the pressure—volume response of elastomers in hydrostatic compression, as well as the stress—stretch and volume change—stretch data of elastomers in uniaxial tension.

Nonlinear Constitutive Models and the Finite Element Absolute Nodal Coordinate Formulation

2007 ◽  
Author(s):  
Luis G. Maqueda ◽  
Ahmed A. Shabana
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Constitutive Models ◽  
Biological Tissues ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Deformation Analysis ◽  
Absolute Nodal Coordinate ◽  
The Absolute ◽  
Nonlinear Constitutive Models ◽  
Nonlinear Elastic

In this investigation, the use of three different nonlinear constitutive models based on the hyper-elasticity theory with the absolute nodal coordinate formulation is considered. These three nonlinear constitutive models are based on the Neo-Hookean constitutive law for compressible materials, the Neo-Hookean constitutive law for incompressible materials, and the Mooney-Rivlin constitutive law in which the material is assumed to be incompressible. These models, which allow capturing Poisson modes, are suitable for many materials and applications, including rubber-like materials and biological tissues which are governed by nonlinear elastic behavior and are considered incompressible or nearly incompressible. Numerical examples that demonstrate the implementation of these nonlinear constitutive models in the absolute nodal coordinate formulation are presented. The results obtained using the nonlinear and linear constitutive models are compared in this study. The results show that when linear constitutive models are used in the large deformation analysis, singular configurations are encountered and basic formulas such as Nanson’s formula are no longer valid. These singular deformation configurations are not encountered when the nonlinear constitutive models are used.

Constitutive Law of Finite Deformation Elastoplasticity With Proportional Loadings

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
H. Darijani ◽  
R. Naghdabadi
Keyword(s):  
Constitutive Equation ◽  
Finite Deformation ◽  
Constitutive Models ◽  
Pressure Vessels ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Proportional Loading ◽  
Von Mises ◽  
Plastic Parts

In this paper, decomposition of the total strain into elastic and plastic parts is investigated for extension of elastic-type constitutive models to finite deformation elastoplasticity. In order to model the elastic behavior, a Hookean-type constitutive equation based on the logarithmic strain is considered. Based on this constitutive equation and assuming the deformation theory of Hencky as well as the yield criteria of von Mises, the elastic-plastic behavior of materials at finite deformation is modeled in the case of the proportional loading. Moreover, this elastoplastic model is applied in order to determine the stress distribution in thick-walled cylindrical pressure vessels at finite deformation elastoplasticity.

Applicability of Duncan-Chang Model and its Modified Versions to Methane Hydrate-Bearing Sands

2011 ◽  
Vol 347-353 ◽  
pp. 3384-3387 ◽  
Author(s):  
Ju Hua Xiong ◽  
Xiao Yong Kou ◽  
Fang Liu ◽  
Ming Jing Jiang
Keyword(s):  
Methane Hydrate ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Triaxial Tests ◽  
Elastic Model ◽  
Clathrate Compound ◽  
Constitutive Response ◽  
Nonlinear Elastic ◽  
Hydrate Bearing Sediments ◽  
Chang Model

Methane hydrate is ice-like clathrate compound that attracts global attention due to its huge potential as a future energy source. The constitutive law of methane hydrate-bearing sediments remains unknown and becomes a barrier in sustainable exploitation of methane hydrate from marine sediments. The Duncan-Change model is a nonlinear elastic model which was widely accepted by the geotechnical community in approximating the constitutive response of geo-materials. This model and its evolved versions were employed in this study to model the stress-strain response observed in triaxial tests on methane hydrate-bearing sands. Duncan-Chang type models capture well the strain hardening behaviors. However, they fall short of incorporating the dependency of temperature and saturation degree of methane hydrate, which have to be taken into account in future constitutive models of methane hydrate-bearing deposits.

Development of a Multibody Model to Predict the Settling Point and Interfacial Pressure Distribution in a Seat–Occupant System

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Yousof Azizi ◽  
Tarun Puri ◽  
Anil K. Bajaj ◽  
Patricia Davies
Keyword(s):  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Elastic Behavior ◽  
Type Model ◽  
Model Parameters ◽  
Force Distribution ◽  
Compression Tests ◽  
Static Compression ◽  
Multibody Model ◽  
Nonlinear Elastic

The location of the hip-joint (H-Point) of a seat occupant is an important design specification which directly affects the seat static comfort. Most car seats are made of polyurethane foam and so the location of the H-Point is dependent on the quasi-static behavior of foam. In this research, a previously developed model of the seat–occupant system is refined by incorporating an improved foam model which is used to study seat and occupant interactions and the location of occupant’s H-Point. The seat is represented by a series of discrete nonlinear viscoelastic elements that characterize the seating foam behavior. The nonlinear elastic behavior of these elements is expressed by a higher order polynomial while their viscoelastic behavior is described by a hereditary type model with parameters that are functions of the compression rate. The nonlinear elastic and viscoelastic model parameters were estimated previously using data obtained from a series of quasi-static compression tests on a car seat foam sample. The occupant behavior is described by a constrained two-dimensional multibody model with five degrees of freedom. A Lagrangian formulation is used to derive the governing equations for the seat–occupant model. These differential equations are solved numerically to obtain the H-Point location. These results are then used to calculate the force distribution at the seat and occupant interfaces. The force distribution at the seat–occupant interface is also investigated experimentally and is found to match qualitatively with the results obtained using the seat–occupant model.

Nonlinear Elastic Behavior of Unidirectional Composites With Fiber Waviness Under Compressive Loading

1996 ◽  
Vol 118 (4) ◽  
pp. 561-570 ◽  
Author(s):  
H. M. Hsiao ◽  
I. M. Daniel
Keyword(s):  
Constitutive Relations ◽  
Compressive Loading ◽  
Nonlinear Material ◽  
Elastic Behavior ◽  
Compression Tests ◽  
Fiber Waviness ◽  
Unidirectional Composites ◽  
Nonlinear Stress ◽  
Material Nonlinear ◽  
Nonlinear Elastic

Nonlinear elastic behavior of unidirectional composites with fiber waviness under compressive loading was investigated theoretically and experimentally. Unidirectional carbon/epoxy composites with uniform, graded, and localized fiber waviness were studied. Complementary strain energy was used to derive the material nonlinear stress-strain relations. Nonlinear material properties obtained from shear and longitudinal and transverse compression tests were incorporated into the analysis. Compression tests of specimens with known fiber waviness were conducted to verify the constitutive relations. Experimental results were in good agreement with predictions based on the constitutive model.

Constitutive Modeling for Flow Stress Behavior of Nimonic 80A Superalloy During Hot Deformation Process

2016 ◽  
Vol 35 (3) ◽  
pp. 327-336 ◽  
Author(s):  
Sendong Gu ◽  
Liwen Zhang ◽  
Chi Zhang ◽  
Wenfei Shen
Keyword(s):  
Flow Stress ◽  
Constitutive Model ◽  
Hot Deformation ◽  
Critical Strain ◽  
Volume Fraction ◽  
Constitutive Models ◽  
Avrami Equation ◽  
Peak Strain ◽  
Compression Tests ◽  
Nimonic 80A

AbstractThe hot deformation characteristics of nickel-based alloy Nimonic 80A were investigated by isothermal compression tests conducted in the temperature range of 1,000–1,200°C and the strain rate range of 0.01—5 s–1on a Gleeble-1500 thermomechanical simulator. In order to establish the constitutive models for dynamic recrystallization (DRX) behavior and flow stress of Nimonic 80A, the material constantsα,nand DRX activation energyQin the constitutive models were calculated by the regression analysis of the experimental data. The dependences of initial stress, saturation stress, steady-state stress, dynamic recovery (DRV) parameter, peak strain, critical strain and DRX grain size on deformation parameters were obtained. Then, the Avrami equation including the critical strain for DRX and the peak strain as a function of strain was established to describe the DRX volume fraction. Finally, the constitutive model for flow stress of Nimonic 80A was developed in DRV region and DRX region, respectively. The flow stress values predicted by the constitutive model are in good agreement with the experimental ones, which indicates that the constitutive model can give an accurate estimate for the flow stress of Nimonic 80A under the deformation conditions.

Modeling Method of Constitutive Law of Rubber Hyperelasticity Based on Finite Element Simulations

2003 ◽  
Vol 76 (1) ◽  
pp. 271-285 ◽  
Author(s):  
Li-Rong Wang ◽  
Zhen-Hua Lu
Keyword(s):  
Finite Element ◽  
Finite Element Simulations ◽  
Constitutive Law ◽  
Modeling Technique ◽  
Characteristic Analysis ◽  
Rubber Material ◽  
Element Simulation ◽  
Tension And Compression ◽  
Nonlinear Elastic ◽  
Elastic Characteristics

Abstract This paper is to present a method and procedure for modeling the constitutive law of anti-vibration rubber hyperelasticity based on finite element simulations. The hyperelasticity of rubber-like material is briefly summarized first. Then a method and procedure for determining an accurate constitutive law of rubber hyperelasticity from uniaxial tension and compression experiment data is presented and implemented. Due to nonlinear elastic properties of rubber and application limitations of various forms of constitutive law, results of finite element simulation to rubber material experiments show that different forms of constitutive law have to be adopted in different ranges of strain. The proposed procedure to obtain an appropriate constitutive law of rubber hyperelasticity of vibration isolator provides engineers with an effective modeling technique for design and analysis of anti-vibration rubber components. Finally, models of three kinds of rubber materials of a hydraulically damped rubber mount (HDM) are determined by tests and finite element simulations and applied to static and dynamic characteristic analysis of the HDM. The predicted elastic characteristics of the HDM and its major rubber components agree well with experimental data, which demonstrates the practicability and effectiveness of the presented modeling technique to modeling engineering rubber materials in dynamic systems.

Uncertainty Quantification in Predicting Behaviour of Rubber-Like Materials in Uni-Axial Loading

2020 ◽  
Author(s):  
Aref Ghaderi ◽  
Vahid Morovati ◽  
Pouyan Nasiri ◽  
Roozbeh Dargazany
Keyword(s):  
Uncertainty Quantification ◽  
Mechanical Response ◽  
Pure Shear ◽  
Constitutive Models ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Deterministic Models ◽  
Data Set ◽  
Material Parameters ◽  
Axial Extension

Abstract Material parameters related to deterministic models can have different values due to variation of experiments outcome. From a mathematical point of view, probabilistic modeling can improve this problem. It means that material parameters of constitutive models can be characterized as random variables with a probability distribution. To this end, we propose a constitutive models of rubber-like materials based on uncertainty quantification (UQ) approach. UQ reduces uncertainties in both computational and real-world applications. Constitutive models in elastomers play a crucial role in both science and industry due to their unique hyper-elastic behavior under different loading conditions (uni-axial extension, biaxial, or pure shear). Here our goal is to model the uncertainty in constitutive models of elastomers, and accordingly, identify sensitive parameters that we highly contribute to model uncertainty and error. Modern UQ models can be implemented to use the physics of the problem compared to black-box machine learning approaches that uses data only. In this research, we propagate uncertainty through the model, characterize sensitivity of material behavior to show the importance of each parameter for uncertainty reduction. To this end, we utilized Bayesian rules to develop a model considering uncertainty in the mechanical response of elastomers. As an important assumption, we believe that our measurements are around the model prediction, but it is contaminated by Gaussian noise. We can make the noise by maximizing the posterior. The uni-axial extension experimental data set is used to calibrate the model and propagate uncertainty in this research.

scholarly journals Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Reference Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Flexible Beam ◽  
Beam Model ◽  
Beam Structures ◽  
Nodal Displacements ◽  
Nonlinear Constitutive Law

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

scholarly journals A set of measures for the systematic classification of the nonlinear elastic behavior of disparate rocks

2015 ◽  
Vol 120 (3) ◽  
pp. 1587-1604 ◽  
Author(s):  
Jacques Rivière ◽  
Parisa Shokouhi ◽  
Robert A. Guyer ◽  
Paul A. Johnson
Keyword(s):  
Elastic Behavior ◽  
Systematic Classification ◽  
Nonlinear Elastic
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