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.

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.

A Study on the Material Modeling of a Robot Polyurethane Stopper

2009 ◽  
Author(s):  
Kyukwon Bang ◽  
Taewung Kim ◽  
Hyun-Yong Jeong
Keyword(s):  
Finite Element ◽  
Shear Test ◽  
Pure Shear ◽  
Material Model ◽  
Tension Test ◽  
Material Behavior ◽  
Prony Series ◽  
Material Constants ◽  
Torsion Vibration ◽  
Element Simulation

Polyurethane stoppers are used to protect heavy parts from damage in case of an unpredicted impact between parts in a robot. In order to evaluate the performance of a polyurethane stopper during impact, it was necessary to model the material behavior. Thus, the compression test, the tension test, the pure shear test, the torsion vibration test were conducted, and the hyperelastic material constants and viscoelastic material constants (Prony series parameters) were determined. Finite element simulations for the tests were conducted to check whether the material model adequately represented the material behavior. In addition, a finite element simulation for an impact between a part of a robot and a stopper was conducted to evaluate the performance of a stopper.

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 FINITE ELEMENT IMPLEMENTATION OF GEOMETRICALLY NONLINEAR CONTACT

2021 ◽  
Vol 30 ◽  
pp. 18-23
Author(s):  
Ondřej Faltus ◽  
Martin Horák
Keyword(s):  
Finite Element ◽  
Large Strain ◽  
Small Strain ◽  
Geometrically Nonlinear ◽  
Finite Element Software ◽  
Finite Element Implementation ◽  
Algorithmic Solution ◽  
Code Base ◽  
Nonlinear Contact ◽  
Current Code

The OOFEM finite element software has been recently updated to include contact algorithms for small strain applications. In this work, we attempt to extend the contact algorithms to large strain problems. Reviewing the current code and comparing it with approaches encountered in literature, we arrive at a specific algorithmic solution and integrate it into the current code base. The current code is explained, the necessary extensions are derived and documented, and the algorithmic changes are described. Tests confirm the functionality and quadratic rate of convergence of the proposed implementation.

Texture Based Finite Element Simulation of a Two-Step Can Forming Process

2012 ◽  
Vol 504-506 ◽  
pp. 655-660 ◽  
Author(s):  
Vedran Glavas ◽  
Thomas Böhlke ◽  
Dominique Daniel ◽  
Christian Leppin
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Plastic Material ◽  
Large Strain ◽  
Material Model ◽  
Material Behavior ◽  
Flow Rule ◽  
Forming Process ◽  
Aluminum Sheets ◽  
Element Simulation

Aluminum sheets used for beverage cans show a significant anisotropic plastic material behavior in sheet metal forming operations. In a deep drawing process of cups this anisotropy leads to a non-uniform height, i.e., an earing profile. The prediction of this earing profiles is important for the optimization of the forming process. In most cases the earing behavior cannot be predicted precisely based on phenomenological material models. In the presented work a micromechanical, texture-based model is used to simulate the first two steps (cupping and redrawing) of a can forming process. The predictions of the earing profile after each step are compared to experimental data. The mechanical modeling is done with a large strain elastic visco-plastic crystal plasticity material model with Norton type flow rule for each crystal. The response of the polycrystal is approximated by a Taylor type homogenization scheme. The simulations are carried out in the framework of the finite element method. The shape of the earing profile from the finite element simulation is compared to experimental profiles.

Non-Conservative and Conservative Loads in Geometrically Nonlinear Shells

2003 ◽  
Author(s):  
Cho W. S. To ◽  
Meilan L. Liu
Keyword(s):  
Finite Element ◽  
Large Strain ◽  
Small Strain ◽  
Shell Structures ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Hybrid Strain ◽  
Shell Elements ◽  
Updated Lagrangian Formulation ◽  
Updated Lagrangian

Responses of geometrically nonlinear shell structures under combined conservative and non-conservative loads are investigated and presented in this paper. The shell structures are discretized by the finite element method and represented by the hybrid strain based three node flat triangular shell elements that were developed previously by the authors. The updated Lagrangian formulation and the incremental Hellinger-Reissner variational principle are employed. Features such as large or small strain deformation, finite rotation, updated thickness so as to account for the “thinning effect” due to large strain deformation, and inclusion or exclusion of the mid-surface director field are incorporated in the finite element formulation. Representative results of two examples are included to demonstrate the capability, accuracy and efficiency of the computational strategy proposed.

A Generalized Finite Element Analysis of Sheet Metal Forming With an Elastic-Viscoplastic Material Model

1986 ◽  
Vol 108 (1) ◽  
pp. 9-15 ◽  
Author(s):  
A. Chandra
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Large Strain ◽  
Present Report ◽  
Material Behavior ◽  
Large Strains ◽  
Element Analysis

A finite element analysis for elastic-viscoplastic problems in the presence of large strains is presented in this paper. The formulation is capable of using any of a class of combined creep-plasticity constitutive models with state variables for the description of material behavior. The specific problem considered is plane strain sheet metal forming using the constitutive model originally proposed by Hart. Numerical results are presented for sample problems and the effects of variations in several process parameters, such as velocity, friction at punch, and die interfaces, are investigated. The present report includes membrane, bending, and shear effects as well as the coupling among them and no a priori assumption is made about the strain distribution across the thickness. Thus, it unifies the earlier approaches used in sheet metal forming analysis and helps in gaining crucial insights into the process of sheet metal forming. It can also be extended to other large strain design and manufacturing problems.

Elastic-Plastic Analysis for Cracked Members

1976 ◽  
Vol 98 (1) ◽  
pp. 47-55 ◽  
Author(s):  
P. D. Hilton
Keyword(s):  
Finite Element ◽  
Small Strain ◽  
Material Behavior ◽  
Uniaxial Tensile ◽  
Crack Face ◽  
Exterior Surface ◽  
Elastic Plastic ◽  
Finite Element Procedure ◽  
Hollow Cylindrical Specimen ◽  
Cracked Specimens

Elastic-plastic finite element analyses are performed for cracked specimens of various geometries and material properties. The calculations are based on the small strain, J2-deformation theory of plasticity; employing a power hardening model for the material behavior under uniaxial tensile loading. The finite element procedure includes the use of a specialized plastic, crack tip singularity element; and, it is applicable to the geometric idealizations of plane stress, plane strain, and axial symmetry. Results are presented for tensile and bending specimens containing exterior cracks and for a hollow cylindrical specimen with a circumferential crack subjected to tensile and pressure loading. Numerical values are reported for the plastic intensity factor, the crack face separation at the exterior surface, and the J-integral. Both the implications of these results to fracture prediction and the limitations on their applicability as a consequence of geometric and material modeling idealizations are discussed.

Mechanical characterization and finite element modeling of polylactic acid BCC-Z cellular lattice structures fabricated by fused deposition modeling

2016 ◽  
Vol 231 (11) ◽  
pp. 1995-2004 ◽  
Author(s):  
R Rezaei ◽  
MR Karamooz Ravari ◽  
M Badrossamay ◽  
M Kadkhodaei
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Polylactic Acid ◽  
Fused Deposition Modeling ◽  
Material Behavior ◽  
Lattice Structures ◽  
Stress Strain ◽  
Fused Deposition ◽  
Tension And Compression ◽  
Deposition Modeling

In recent years, cellular lattice structures are of interest due to their high strength in combination with low weight. They may be used in various areas such as aerospace and automotive industries. Accordingly, assessment of their manufacturability, repeatability and mechanical properties is very important. In this paper, these issues are investigated for Polylactic Acid cellular lattice structures fabricated by fused deposition modeling. To do so, some benchmarks are designed and fabricated to find suitable processing parameters as well as the structural dimensions. In addition, to evaluate the mechanical properties of the lattice’s material, a number of tension and compression specimens are fabricated and tested. The material’s stress–strain curves reveal non-linear behaviors. These curves are not coincided in tension and compression which shows an asymmetric material behavior. To characterize the fabricated cellular lattices, they are tested in compression, and the deformation mechanisms of the structures are analyzed. To investigate the correlation between the bulk material and the material of the ligaments, a solid finite element model is developed to predict the stress–strain response of the lattice. The obtained result shows a reasonably good correlation between the model and experiments.

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