A Viscohyperelastic Maxwell Model for Rubber Viscoelasticity

1992 ◽  
Vol 65 (1) ◽  
pp. 137-153 ◽  
Author(s):  
A. R. Johnson ◽  
C. J. Quigley
Keyword(s):  
Finite Element ◽  
Strain Relaxation ◽  
Constitutive Models ◽  
Constant Strain Rate ◽  
Maxwell Model ◽  
Large Strains ◽  
The Finite Element Method ◽  
Rate Test ◽  
Pull Tests ◽  
Step Strain

Abstract A new viscoelaslic model for rubber is presented. It is similar in a Maxwell internal solid model in which all the solids are hyperelastic. A key feature of this model is its ability to accurately predict step-strain relaxation test data for very large strains. A method to obtain the constitutive models for the solids is presented for the three legged version and is used with existing data in the literature to compute variable-rate uniaxial pull tests. The finite-element implementation of this theory is given. Computations are made for a uniaxial constant-strain-rate test using a nearly incompressible axisymmetric version of the finite-element method.

scholarly journals Modeling Step—Strain Relaxation and Cyclic Deformations of Elastomers

2002 ◽  
Vol 75 (2) ◽  
pp. 333-345
Author(s):  
A. R. Johnson ◽  
T. Chen ◽  
J. L. Mead
Keyword(s):  
Least Squares Method ◽  
Large Strain ◽  
Strain Relaxation ◽  
Nonlinear Least Squares ◽  
Friction Stress ◽  
Maxwell Model ◽  
Constitutive Theory ◽  
Relaxation Data ◽  
Nonlinear Least Squares Method ◽  
Step Strain

Abstract Data for step—strain relaxation and cyclic compressive deformations of highly viscous short elastomer cylinders are modeled using a large strain rubber viscoelastic constitutive theory with a rate—independent friction stress term added. In the tests, both small and large amplitude cyclic compressive strains, in the range of 1% to 10%, were superimposed on steady state compressed strains, in the range of 5% to 20%, for frequencies of 1 and 10 Hz. The elastomer cylinders were conditioned prior to each test to soften them. The constants in the viscoelastic—friction constitutive theory are determined by employing a nonlinear least-squares method to fit the analytical stresses for a Maxwell model, which includes friction, to measured relaxation stresses obtained from a 20% step—strain compression test. The simulation of the relaxation data with the nonlinear model is successful at compressive strains of 5%, 10%, 15%, and 20%. Simulations of hysteresis stresses for enforced cyclic compressive strains of 20%±5% are made with the model calibrated by the relaxation data. The predicted hysteresis stresses are lower than the measured stresses.

scholarly journals The Strength of Egg Trays under Compression: A Numerical and Experimental Study

Materials ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2279
Author(s):  
Leszek Czechowski ◽  
Gabriela Kmita-Fudalej ◽  
Włodzimierz Szewczyk
Keyword(s):  
Finite Element Method ◽  
Experimental Study ◽  
Finite Element ◽  
Maximum Load ◽  
Experimental Investigations ◽  
Large Strains ◽  
Strength Ratio ◽  
The Finite Element Method ◽  
Compression Stiffness ◽  
Different Shapes

This work concerns the analysis of egg packages subjected to compression. Experimental investigations were carried out to determine the curves of compression and maximum loads. To compare packages accessible on the market, several different shapes of egg packages were tested after being conditioned in air with a relative humidity of 50%. Several paper structures in stock were compressed. By validating the experiment results, numerical computations based on the finite element method (FEM) were executed. The estimations of a numerical model were performed with the use of the perfect plasticity of paper and with the assumption of large strains and deflections. Our own two structures of egg packaging were taken into account: basic and modified. The material of the packages was composed of 90% recovered paper and 10% coconut fibres. This paper involved the numerical modelling of such complex packaging. Moreover, our research showed that introducing several features into the structures of the packaging can improve the stiffness and raise the maximum load. Thanks to the application of ribs and grooves, the strength ratio and compression stiffness, in comparison to the basic tray, increased by approximately 23.4% and 36%, respectively. Moreover, the obtained indexes of modified trays were higher than the majority of the studied market trays.

scholarly journals Predicting Nonlinear and Anisotropic Mechanics of Metal Rubber Using a Combination of Constitutive Modeling, Machine Learning, and Finite Element Analysis

Materials ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5200
Author(s):  
Yalei Zhao ◽  
Hui Yan ◽  
Yiming Wang ◽  
Tianyi Jiang ◽  
Hongyuan Jiang
Keyword(s):  
Finite Element ◽  
Constitutive Modeling ◽  
Constitutive Models ◽  
Finite Element Method Simulation ◽  
Ann Model ◽  
The Finite Element Method ◽  
Functional Material ◽  
Element Analysis ◽  
Metal Rubber ◽  
Artificial Neural Network Ann

Metal rubber (MR) is an entangled fibrous functional material, and its mechanical properties are crucial for its applications; however, numerical constitutive models of MR for prediction and calculation are currently undeveloped. In this work, we provide a numerical constitutive model to express the mechanics of MR materials and develop an efficient finite elements method (FEM) to calculate the performance of MR components. We analyze the nonlinearity and anisotropy characteristics of MR during the deformation process. The elasticity matrix is adopted to express the nonlinearity and anisotropy of MR. An artificial neural network (ANN) model is built, trained, and tested to output the current elastic moduli for the elasticity matrix. Then, we combine the constitutive ANN model with the finite element method simulation to calculate the mechanics of the MR component. Finally, we perform a series of static and shock experiments and finite element simulations of an MR isolator. The results demonstrate the feasibility and accuracy of the numerical constitutive MR model. This work provides an efficient and convenient method for the design and analysis of MR components.

Viscohyperelastic Modeling of Rubber Vulcanizates

1993 ◽  
Vol 21 (3) ◽  
pp. 179-199 ◽  
Author(s):  
A. R. Johnson ◽  
C. J. Quigley ◽  
D. G. Young ◽  
J. A. Danik
Keyword(s):  
Energy Function ◽  
Strain Relaxation ◽  
Cyclic Strain ◽  
Rate Of Change ◽  
Large Strains ◽  
Energy Functions ◽  
Relaxation Parameters ◽  
The Difference ◽  
Experimental Values ◽  
Step Strain

Abstract The use of internal hyperelastic solids for modeling viscoelastic deformations of rubber vulcanizates is reviewed. The model is applied in one dimension to viscoelastic uniaxial tension and uniaxial shear experiments. Step-strain relaxation tests are used to determine the model's parameters. A hyperelastic energy function, which represents the sum of the internal solids' energy functions, is obtained by least squares fitting a constrained third-order invariant expansion of the Rivlin function to the difference between the step-strain stresses and the relaxed stresses (the standard hyperelastic solid's stresses). The difference energy function is split into two parts and relaxation parameters (related to the rate of change of the internal solids' reference lengths) are selected so that numerically simulated step-strain relaxation stresses approximate the experimental values (at approximately 50 ms). The model is then used to predict the experimental results from a different type of test, cyclic strain data, at three different strain rates (cyclic frequencies). Increased stress due to increased strain rate was indicated by the model for large strains.

Implementation of Material Stiffness Coefficients in Finite Element Applications to Rubber

1994 ◽  
Vol 22 (4) ◽  
pp. 223-241 ◽  
Author(s):  
Y. Kim ◽  
A. F. Saleeb ◽  
T. Y. P. Chang
Keyword(s):  
Finite Element ◽  
Constitutive Models ◽  
The Finite Element Method ◽  
Stiffness Coefficients ◽  
Material Stiffness ◽  
Nonlinear Curve Fitting ◽  
Principal Value ◽  
General Strain ◽  
Fitting In ◽  
Nonlinear Curve

Abstract Two classes of constitutive models are widely used in the current literature to describe the general strain state of rubber under large deformations: the Invariant-based (Rivlin type) and the Principal-value based (Ogden type). However, their predictive capabilities, coupled with the finite element method, will greatly depend on the material coefficients determined from experimental stress-strain curves by nonlinear curve fitting. In addition, special care must be exercised in their numerical implementations, which is particularly true for the Ogden type models, when evaluating the material tangent stiffness coefficients. Several issues in connection with these are discussed and a number of simulations and test comparisons are presented.

Large Strain Viscoelastic Constitutive Models for Rubber, Part II: Determination of Material Constants

1995 ◽  
Vol 68 (2) ◽  
pp. 230-247 ◽  
Author(s):  
Claudia J. Quigley ◽  
Joey Mead ◽  
Arthur R. Johnson
Keyword(s):  
Finite Element ◽  
Large Strain ◽  
Strain Relaxation ◽  
Small Strain ◽  
Material Behavior ◽  
Prony Series ◽  
Relaxation Data ◽  
Material Constants ◽  
Tension And Compression ◽  
Step Strain

Abstract A method for determining material constants in large strain viscoelastic materials was demonstrated for a highly saturated nitrile rubber. Material constant selection was based on viscoelastic stress relaxation data at small and large strains, under both tension and compression, and was constrained to assure Drucker stability. Assuming that the viscoelastic strain energy function was both time and strain separable, a Prony series was constructed for the time dependent material constants. For comparison, four different Prony series were developed from collocation methods and a nonlinear regression analysis, each separately based on either large or small tensile strain relaxation data. In addition, a final Prony series was constructed from dynamic data. These Prony series were included in this comparison to judge their ability to predict both large and small strain material behavior. Finite element analyses of large and small step-strain relaxation tests and a single cycle hysteresis loop at large deformations were performed for each set of Prony series. The results were then compared to experimental behavior. The Prony series based on the constrained method accurately predicted step-strain relaxation behavior at all strain levels, for both tension and compression. The finite element results for the other Prony series show that large strain material behavior was best predicted by those Prony series based on large strain material behavior. Similar findings were found for small strain material behavior. The constrained Prony series and the two large strain based Prony series best modeled the experimental hysteresis loop.

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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