A variable-order viscoelastic constitutive model under constant strain rate

2020 ◽  
Author(s):  
Yao Wang ◽  
Dagang Sun ◽  
Zhanlong Li ◽  
Yuan Qin ◽  
Bao Sun
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Fractional Order ◽  
Viscoelastic Material ◽  
Constitutive Models ◽  
Constant Strain Rate ◽  
Variable Order ◽  
Hyper Elastic ◽  
Material Coefficient ◽  
Viscoelastic Coefficient

The traditional viscoelastic constitutive models encounter the problems of massive parameters and ambiguous physical meanings. A new concept of variable-order viscoelastic constitutive (called VOVC) model is put forward based on the constant fractional-order constitutive model and the viscoelastic theory. The determination methods of the two parameters in the VOVC model, including the material coefficient and the viscoelastic coefficient, are discussed both in the tensile and the resilient processes. The comparisons are made between the VOVC model and the traditional constitutive models i.e. the constant fractional-order Kelvin-Voigt (CFKV) model, the Zhu-wang-tang nonlinear thermo-viscoelastic constitutive (ZWT) model and the Ogden nonlinear hyper-elastic (Ogden) model. The results show that the VOVC model with the constant material coefficient and the variable viscoelastic coefficient predicts the whole evolution of the constitutive behavior of the viscoelastic material under the constant strain rate more precisely. The constant material coefficient in the VOVC model means the stiffness of the viscoelastic material. The variable viscoelastic coefficient in the model means the distribution of the elasticity and viscosity. The VOVC model contains a simpler structure, fewer parameters, clearer physical meanings and higher precision.

Fractional Order Constitutive Model of Geomaterials Under the Condition of Triaxial Test

2011 ◽  
Author(s):  
Deshun Yin ◽  
Hao Wu ◽  
Chen Cheng ◽  
YangQuan Chen
Keyword(s):  
Fractional Calculus ◽  
Constitutive Model ◽  
Fractional Order ◽  
Triaxial Test ◽  
Constitutive Models ◽  
Constant Strain Rate ◽  
Stress Strain ◽  
Good Tool ◽  
Strain Relation ◽  
Stress Strain Relation

Fractional calculus has been successfully applied to characterize the rheological property of viscoelastic materials, however, geomaterials were seldom involved in fractional order constitutive models (FOCM), and the issue of first loading and then unloading is rarely discussed through fractional calculus. It is considered that all materials are arranged in a queue and ideal solid and Newtonian fluid are located at both ends of the queue in FOCM. On the basis of FOCM, stress-strain relation under the condition of first loading and then unloading, besides creep, stress-relaxation and loading of constant strain rate are obtained. The stress-strain relation is utilized to fit triaxial test results of geomaterials under the corresponding conditions. The comparison between the test and fitting results reveals that FOCM can reasonably describe the stress-strain, stress-time or strain-time characteristics of geomaterials, which shows that fractional calculus is a good tool to constitutive model research of geomaterials.

Experimental and Numerical Study of Soft Tissue Surrogate Behavior Under Ballistic Loading

2012 ◽  
Author(s):  
Ericka K. Amborn ◽  
Karim H. Muci-Küchler ◽  
Brandon J. Hinz
Keyword(s):  
Soft Tissue ◽  
Constitutive Model ◽  
High Strain Rate ◽  
Strain Rate ◽  
High Strain ◽  
Split Hopkinson Pressure Bar ◽  
Numerical Study ◽  
Constitutive Models ◽  
Material Behavior ◽  
Good Representation

Studying the high strain rate behavior of soft tissues and soft tissue surrogates is of interest to improve the understanding of injury mechanisms during blast and impact events. Tests such as the split Hopkinson pressure bar have been successfully used to characterize material behavior at high strain rates under simple loading conditions. However, experiments involving more complex stress states are needed for the validation of constitutive models and numerical simulation techniques for fast transient events. In particular, for the case of ballistic injuries, controlled tests that can better reflect the effects induced by a penetrating projectile are of interest. This paper presents an experiment that tries to achieve that goal. The experimental setup involves a cylindrical test sample made of a translucent soft tissue surrogate that has a small pre-made cylindrical channel along its axis. A small caliber projectile is fired through the pre-made channel at representative speeds using an air rifle. High speed video is used in conjunction with specialized software to generate data for model validation. A Lagrangian Finite Element Method (FEM) model was prepared in ABAQUS/Explicit to simulate the experiments. Different hyperelastic constitutive models were explored to represent the behavior of the soft tissue surrogate and the required material properties were obtained from high strain rate test data reported in the open literature. The simulation results corresponding to each constitutive model considered were qualitatively compared against the experimental data for a single projectile speed. The constitutive model that provided the closest match was then used to perform an additional simulation at a different projectile velocity and quantitative comparisons between numerical and experimental results were made. The comparisons showed that the Marlow hyperelastic model available in ABAQUS/Explicit was able to produce a good representation of the soft tissue surrogate behavior observed experimentally at the two projectile speeds considered.

Tensile Stress-Strain Curves Modeling of Four Kinds of Solders with Temperature and Rate Dependence

2005 ◽  
Vol 297-300 ◽  
pp. 905-911 ◽  
Author(s):  
Xu Chen ◽  
Li Zhang ◽  
Masao Sakane ◽  
Haruo Nose
Keyword(s):  
Tensile Stress ◽  
Constitutive Model ◽  
Strain Rate ◽  
Constant Strain Rate ◽  
Tensile Tests ◽  
Strain Rate Range ◽  
Rate Dependence ◽  
Strain Rates ◽  
Stress Strain ◽  
Rate Range

A series of tensile tests at constant strain rate were conducted on tin-lead based solders with different Sn content under wide ranges of temperatures and strain rates. It was shown that the stress-strain relationships had strong temperature- and strain rate- dependence. The parameters of Anand model for four solders were determined. The four solders were 60Sn-40Pb, 40Sn-60Pb, 10Sn-90Pb and 5Sn-95Pb. Anand constitutive model was employed to simulate the stress-strain behaviors of the solders for the temperature range from 313K to 398K and the strain rate range from 0.001%sP -1 P to 2%sP -1 P. The results showed that Anand model can adequately predict the rate- and temperature- related constitutive behaviors at all test temperatures and strain rates.

Development of “Material Specific” Creep Continuum Damage Mechanics-Based Constitutive Equations

2020 ◽  
Author(s):  
Ricardo Vega ◽  
Jaime A. Cano ◽  
Calvin M. Stewart
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Creep Strain ◽  
Creep Deformation ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Constitutive Models ◽  
Continuum Damage Mechanics ◽  
Creep Strain Rate ◽  
Continuum Damage

Abstract The objective of this study is to introduce a method for creating “material specific” creep continuum damage mechanics-based constitutive models. Herein, material specific is defined as a constitutive model based on the mechanism-informed minimum creep strain rate (MCSR) equations found in deformation mechanism maps and calibrated to available material data. The material specific models are created by finding the best MCSR model for a dataset. Once the best MCSR model is found, the Monkman Grant inverse relationship between the MCSR and rupture time is employed to derive a rupture equation. The equations are substituted into continuum damage mechanics-based creep strain rate and damage evolution equations to furnish predictions of creep deformation and damage. Material specific modeling allows for the derivation of creep constitutive models that can better the material behavior specific to the available data of a material. The material specific framework is also advantageous since it has a systematic framework that moves from finding the best MCSR model, to rupture time, to damage evolution and, creep strain rate. Data for Alloy P91 was evaluated and a material specific constitutive model derived. The material specific model was able to accurately predict the MCSR, creep deformation, damage, and rupture of alloy P91.

A Phenomenological Constitutive Model Constructed for PC/ABS Blends

2006 ◽  
Vol 306-308 ◽  
pp. 989-994 ◽  
Author(s):  
M. Nizar Machmud ◽  
Masaki Omiya ◽  
Hirotsugu Inoue ◽  
Kikuo Kishimoto
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Constitutive Models ◽  
Strain Rates ◽  
Strain Behavior ◽  
Tension Tests ◽  
Proposed Model ◽  
Wide Range ◽  
Different Temperatures ◽  
Prediction Evaluation

Based on previous available constitutive models, a phenomenological constitutive model has been constructed and is proposed to describe the strain, strain rate and temperature dependentdeformation behavior of PC/ABS blends. In this paper, four quasi-static uniaxial tension tests of a specimen tested at different strain rates and temperatures were used to identify the constitutive model constants. By using the proposed constitutive model, predicting the stress-strain behavior of the PC/ABS blend tested at certain strain rate and different temperatures compares well to the behavior exhibited from the tests. From comparison between the DSGZ and the proposed models, proposed model shows a better prediction. Evaluation of the proposed constitutive model was also presented and it has revealed that the proposed model might have a potential to be used for predicting a wide range of temperatures and high strain rates behavior of PC/ABS blends.

Parameter Evaluation for a Unified Constitutive Model

1993 ◽  
Vol 115 (2) ◽  
pp. 157-162 ◽  
Author(s):  
P. E. Senseny ◽  
N. S. Brodsky ◽  
K. L. DeVries
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Least Squares ◽  
Constitutive Equations ◽  
Laboratory Data ◽  
Constant Strain Rate ◽  
Nonlinear Least Squares ◽  
Evolutionary Equation ◽  
Internal Variables ◽  
Isotropic Hardening

Parameters for the unified constitutive model MATMOD [1] were evaluated for rock salt (NaCl) by using nonlinear least squares to fit the model to isothermal laboratory data. MATMOD incorporates two internal variables that represent the effects of both kinematic and isotropic hardening. The constitutive equations contain nine parameters that must be evaluated to model isothermal deformation. Laboratory data from stress relaxation, constant strain rate, and long-term creep tests were used. The latter two test types included staged tests in which the strain rate or stress was changed step-wise during the test. The test conditions were precisely controlled by a computer and the constitutive equations were integrated to simulate the laboratory conditions closely. The MATMOD parameters were then evaluated by fitting the integrated equations to the laboratory data using nonlinear least squares. The model fits the data well, but the fit may be improved by changing the evolutionary equation for the internal variable that accounts for isotropic hardening.

Deformation Behaviors and Constitutive Model of DP1000 under Different Strain Rates

2017 ◽  
Vol 898 ◽  
pp. 810-817 ◽  
Author(s):  
Ran Wei ◽  
Ren Bo Song ◽  
Long Jiang ◽  
Heng Jun Cai
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Strain Hardening ◽  
Dual Phase Steel ◽  
Constitutive Models ◽  
Rate Sensitivity ◽  
Dual Phase ◽  
Strain Rates ◽  
Deformation Behaviors ◽  
Means Of Transmission

The DP1000 cold-rolled dual phase steel, the thickness of which is 1.2 mm, was required to do the tensile test under nine different strain rates from 10-4 s-1 to 1000 s-1. The mechanical properties and morphologies of the steel were obtained and analyzed. According to the C-J model, the plastic deformation characteristics of dual phase steel under different strain rates were studied. By means of transmission electron microscope (TEM), the morphologies of ferrite and martensite in the dynamic were observed. Finally, the constitutive models of quasi-static and high strain rate were established by using the modified Johnson-Cook model. The results reveal that DP1000 dual phase steel has obvious strain rate sensitivity, and it is a relatively pure ferrite and martensite dual phase structure. There are two stage strain hardenging characteristics in DP1000. In the first stage, the strain hardening ability of ferrite is higher, and the second stage is martensite deformation stage, the strain hardening ability is lower. The modified J-C constitutive model has high fitting effect, and the experimental results are matched with the fitting values.

Pressing Process of Al-W Alloy Powder and Constitutive Model the Pressed Billet at Elevated Temperatures

2014 ◽  
Vol 685 ◽  
pp. 11-17
Author(s):  
Yao Jin Wu ◽  
Yong Xue ◽  
Zhi Ming Zhang ◽  
Ya Wei Huang ◽  
Qian Qian Wang ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Alloy Powder ◽  
Elevated Temperatures ◽  
Testing Machine ◽  
Constant Strain Rate ◽  
Thermal Simulation ◽  
Powder Pressing ◽  
Simulation Testing ◽  
Relation Model

Al-W alloy billets were produced by powder pressing at room temperature and subsequent hot pressing. Quantities of billets were compressed at constant strain rate and temperature with 60% height reduction on Gleeble-3800 thermal simulation testing machine to study the plastic flow behaviors of the test alloy. The temperature of the compression processes ranged from 450 to 570oC. The strain rate was varied between 0.001 and 1s−1. The regularity of flow stress for the test alloy varied at elevated temperatures was studied. The activation energy during hot deformation is 757.943 kJ/mol by calculated, and the Arrhenius constitutive relation model was established. Keywords: Al-W alloy, powder metallurgy, thermal simulation, constitutive model

A New High Strain-Rate Biaxial Experiment to Validate Constitutive Models for Polymers

2016 ◽  
Author(s):  
Sean S. Teller ◽  
Eric C. Schmitt ◽  
Jörgen S. Bergström
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
High Strain Rate ◽  
Strain Rate ◽  
High Strain ◽  
Constitutive Models ◽  
Finite Element Simulations ◽  
Strain Rates ◽  
Peak Strain ◽  
Impact Head

We have developed a new high strain rate experiment in biaxial tension that allows for constitutive model validation at engineering strain rates from 50/s to over 1000/s. In the experiment, a flat disk of the material is clamped at a fixed radial distance. A rail-guided impact sled with a hemispherical impact head is released from the desired height and impacts the disk at the center, potentially deforming the sample to failure. Drop height and impact mass can be varied to modify peak strain rate and impact energy, and the wide range of test conditions allow for testing to be performed on many classes of materials, including thermoplastics and elastomers. The stress and strain fields are calculated using finite element simulations with the proposed constitutive model, and the constitutive model is validated by matching the force versus displacement data of the impact head recorded during experiment to the simulation. In this paper, we discuss results from the experiment and finite element simulations of the experiment on PA (polyamide, nylon) and PEEK (polyether ether ketone). The new experiment allows for validation and refinement of constitutive models, including failure, at high strain rates and in a multiaxial stress state.

scholarly journals Matrix Description of Non-Linear Properties of Materials or Structural Components—Idea and Application Examples

Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5837
Author(s):  
Tomasz Janiak
Keyword(s):  
Numerical Methods ◽  
Constitutive Model ◽  
Matrix Models ◽  
Constitutive Models ◽  
Computer Software ◽  
Physical Nonlinearity ◽  
Analytical Models ◽  
Hyper Elastic ◽  
Properties Of Materials ◽  
Constitutive Matrix

Numerical methods are widely used in structural analysis problems. In the cases of the most complex and practical problems, they are often the only way to obtain solutions, as analytical methods prove ineffective. The motivation for this paper was the desire to extend the scope of numerical methods to cover the problems of creating constitutive models of structural materials. The aim of this research was to develop a matrix or numerical discrete constitutive model of materials. It presents the general assumptions of the developed method for modeling the physical properties of materials. The matrix model is only useful with an appropriate numerical algorithm. Such an algorithm was created and described in this paper. Based on its findings, computer software was developed to perform numerical simulations. Presented calculation examples confirmed the effectiveness of the developed method to create constitutive matrix models of various typical materials, such as steel, but also, e.g., hyper-elastic materials. It also presents the usefulness of constitutive matrix models for simulations of simple stress states and analyses of structural elements such as reinforced concrete. All presented examples involved the physical nonlinearity of the materials. It is proved that the developed matrix constitutive model of materials is efficient and quite versatile. In complex analyses of structures made of nonlinear materials, it can be used as an effective alternative to classical constitutive or analytical models based on elementary mathematical functions.

Sign in / Sign up

Export Citation Format

Share Document