A Constitutive Model Fitting Methodology for Ductile Metals Using Cold Upsetting Tests and Numeric Optimization Techniques

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Devon C. Hartlen ◽  
Darrel A. Doman
Keyword(s):  
Constitutive Model ◽  
Model Fitting ◽  
Frictional Coefficient ◽  
Optimization Techniques ◽  
Model Parameters ◽  
Plastic Behavior ◽  
Radial Deformation ◽  
Plasticity Model ◽  
Cold Upsetting ◽  
Hardening Rule

This work documents the development of a tool to perform automated parameter fitting of constitutive material models. Specific to this work is the fitting of a Swift hardening rule and isotropic linear plasticity model to aluminum 2024-T351, C36000 brass, and C10100 copper. Material characterization was conducted through the use of compressive, cold upsetting tests. A noncontact, optical displacement measurement system was applied to measure the axial and radial deformation of the test specimens. Nonlinear optimization techniques were then applied to tune a finite element model to match experimental results through the optimization of material model parameters as well as frictional coefficient. The result is a system, which can determine constitutive model parameters rapidly and without user interaction. While this tool provided material parameters for each material and model tested, the quality of the fit varied depending on how appropriate the constitutive model was to the material's actual plastic behavior. Aluminum's behavior proved to be an excellent match to the Swift hardening rule while the behavior of brass and copper was described better by the linear plasticity model.

A Simulated Annealing based Optimization Algorithm for Automatic Variogram Model Fitting

2016 ◽  
Vol 61 (3) ◽  
pp. 635-649 ◽  
Author(s):  
Saeed Soltani-Mohammadi ◽  
Mohammad Safa
Keyword(s):  
Simulated Annealing ◽  
Objective Function ◽  
Weighted Least Squares ◽  
Model Fitting ◽  
Optimization Techniques ◽  
Model Parameters ◽  
Model Quality ◽  
Variogram Model ◽  
Fitting Method ◽  
Automatic Fitting

AbstractFitting a theoretical model to an experimental variogram is an important issue in geostatistical studies because if the variogram model parameters are tainted with uncertainty, the latter will spread in the results of estimations and simulations. Although the most popular fitting method is fitting by eye, in some cases use is made of the automatic fitting method on the basis of putting together the geostatistical principles and optimization techniques to: 1) provide a basic model to improve fitting by eye, 2) fit a model to a large number of experimental variograms in a short time, and 3) incorporate the variogram related uncertainty in the model fitting. Effort has been made in this paper to improve the quality of the fitted model by improving the popular objective function (weighted least squares) in the automatic fitting. Also, since the variogram model function (£) and number of structures (m) too affect the model quality, a program has been provided in the MATLAB software that can present optimum nested variogram models using the simulated annealing method. Finally, to select the most desirable model from among the single/multi-structured fitted models, use has been made of the cross-validation method, and the best model has been introduced to the user as the output. In order to check the capability of the proposed objective function and the procedure, 3 case studies have been presented.

Constructing and model-fitting receiver operator characteristics using continuous data.

2018 ◽  
Author(s):  
Josephine Ann Urquhart ◽  
Akira O'Connor
Keyword(s):  
Signal Detection ◽  
Least Squares Method ◽  
Model Fitting ◽  
Simulated Data ◽  
Continuous Variable ◽  
Continuous Data ◽  
Model Parameters ◽  
Operating Characteristics ◽  
Unequal Variance ◽  
Discrete Discrimination

Receiver operating characteristics (ROCs) are plots which provide a visual summary of a classifier’s decision response accuracy at varying discrimination thresholds. Typical practice, particularly within psychological studies, involves plotting an ROC from a limited number of discrete thresholds before fitting signal detection parameters to the plot. We propose that additional insight into decision-making could be gained through increasing ROC resolution, using trial-by-trial measurements derived from a continuous variable, in place of discrete discrimination thresholds. Such continuous ROCs are not yet routinely used in behavioural research, which we attribute to issues of practicality (i.e. the difficulty of applying standard ROC model-fitting methodologies to continuous data). Consequently, the purpose of the current article is to provide a documented method of fitting signal detection parameters to continuous ROCs. This method reliably produces model fits equivalent to the unequal variance least squares method of model-fitting (Yonelinas et al., 1998), irrespective of the number of data points used in ROC construction. We present the suggested method in three main stages: I) building continuous ROCs, II) model-fitting to continuous ROCs and III) extracting model parameters from continuous ROCs. Throughout the article, procedures are demonstrated in Microsoft Excel, using an example continuous variable: reaction time, taken from a single-item recognition memory. Supplementary MATLAB code used for automating our procedures is also presented in Appendix B, with a validation of the procedure using simulated data shown in Appendix C.

scholarly journals Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Steady-State Blood Flow in Microtubes

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 367
Author(s):  
Konstantinos Giannokostas ◽  
Yannis Dimakopoulos ◽  
Andreas Anayiotos ◽  
John Tsamopoulos
Keyword(s):  
Blood Flow ◽  
Steady State ◽  
Constitutive Model ◽  
Blood Plasma ◽  
Constitutive Modeling ◽  
Flow Direction ◽  
Momentum Balance ◽  
Plastic Behavior ◽  
Flow Investigation ◽  
The Impact

The present work focuses on the in-silico investigation of the steady-state blood flow in straight microtubes, incorporating advanced constitutive modeling for human blood and blood plasma. The blood constitutive model accounts for the interplay between thixotropy and elasto-visco-plasticity via a scalar variable that describes the level of the local blood structure at any instance. The constitutive model is enhanced by the non-Newtonian modeling of the plasma phase, which features bulk viscoelasticity. Incorporating microcirculation phenomena such as the cell-free layer (CFL) formation or the Fåhraeus and the Fåhraeus-Lindqvist effects is an indispensable part of the blood flow investigation. The coupling between them and the momentum balance is achieved through correlations based on experimental observations. Notably, we propose a new simplified form for the dependence of the apparent viscosity on the hematocrit that predicts the CFL thickness correctly. Our investigation focuses on the impact of the microtube diameter and the pressure-gradient on velocity profiles, normal and shear viscoelastic stresses, and thixotropic properties. We demonstrate the microstructural configuration of blood in steady-state conditions, revealing that blood is highly aggregated in narrow tubes, promoting a flat velocity profile. Additionally, the proper accounting of the CFL thickness shows that for narrow microtubes, the reduction of discharged hematocrit is significant, which in some cases is up to 70%. At high pressure-gradients, the plasmatic proteins in both regions are extended in the flow direction, developing large axial normal stresses, which are more significant in the core region. We also provide normal stress predictions at both the blood/plasma interface (INS) and the tube wall (WNS), which are difficult to measure experimentally. Both decrease with the tube radius; however, they exhibit significant differences in magnitude and type of variation. INS varies linearly from 4.5 to 2 Pa, while WNS exhibits an exponential decrease taking values from 50 mPa to zero.

scholarly journals A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1393
Author(s):  
Xiaochang Duan ◽  
Hongwei Yuan ◽  
Wei Tang ◽  
Jingjing He ◽  
Xuefei Guan
Keyword(s):  
Composite Materials ◽  
Constitutive Model ◽  
Model Parameters ◽  
Temperature Dependent ◽  
Stress Strain ◽  
Proposed Model ◽  
Single Temperature ◽  
Testing Data ◽  
Bonded Composite ◽  
Tension And Compression

This study develops a general temperature-dependent stress–strain constitutive model for polymer-bonded composite materials, allowing for the prediction of deformation behaviors under tension and compression in the testing temperature range. Laboratory testing of the material specimens in uniaxial tension and compression at multiple temperatures ranging from −40 ∘C to 75 ∘C is performed. The testing data reveal that the stress–strain response can be divided into two general regimes, namely, a short elastic part followed by the plastic part; therefore, the Ramberg–Osgood relationship is proposed to build the stress–strain constitutive model at a single temperature. By correlating the model parameters with the corresponding temperature using a response surface, a general temperature-dependent stress–strain constitutive model is established. The effectiveness and accuracy of the proposed model are validated using several independent sets of testing data and third-party data. The performance of the proposed model is compared with an existing reference model. The validation and comparison results show that the proposed model has a lower number of parameters and yields smaller relative errors. The proposed constitutive model is further implemented as a user material routine in a finite element package. A simple structural example using the developed user material is presented and its accuracy is verified.

scholarly journals Developments in Modelling Bone Screwing

2020 ◽  
Vol 6 (3) ◽  
pp. 111-114
Author(s):  
Jack Wilkie ◽  
Paul D. Docherty ◽  
Knut Möller
Keyword(s):  
Material Properties ◽  
Frictional Coefficient ◽  
Viscous Friction ◽  
Model Parameters ◽  
General Shape ◽  
Bone Material ◽  
Bone Material Properties ◽  
Modelling Methodology ◽  
Recorded Data ◽  
Friction Models

AbstractINTRODUCTION: A torque-rotation model of the bone-screwing process has been proposed. Identification of model parameters using recorded data could potentially be used to determine the material properties of bone. These properties can then be used to recommend tightening torques to avoid over or under-tightening of bone screws. This paper improves an existing model to formulate it in terms of material properties and remove some assumptions. METHOD: The modelling methodology considers a critical torque, which is required to overcome friction and advance the screw into the bone. Below this torque the screw may rotate with elastic deformation of the bone tissue, and above this the screw moves relative to the bone, and the speed is governed by a speed-torque model of the operator’s hand. The model is formulated in terms of elastic modulus, ultimite tensile strength, and frictional coefficient of the bone and the geometry of the screw and hole. RESULTS: The model output shows the speed decreasing and torque increasing as the screw advances into the bone, due to increasing resistance. The general shape of the torque and speed follow the input effort. Compared with the existing model, this model removes the assumption of viscous friction, models the increase in friction as the screw advances into the bone, and is directly in terms of the bone material properties. CONCLUSION: The model presented makes significant improvements on the existing model. However it is intended for use in parameter identification, which was not evaluated here. Further simulation and experimental validation is required to establish the accuracy and fitness of this model for identifying bone material properties.

scholarly journals A Flow Stress Model of 300M Steel for Isothermal Tension

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 252
Author(s):  
Rongchuang Chen ◽  
Shiyang Zhang ◽  
Xianlong Liu ◽  
Fei Feng
Keyword(s):  
Flow Stress ◽  
Constitutive Model ◽  
Tensile Deformation ◽  
Flow Behavior ◽  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Model Parameters ◽  
Average Deviation ◽  
Cross Sectional ◽  
300M Steel

To investigate the effect of hot working parameters on the flow behavior of 300M steel under tension, hot uniaxial tensile tests were implemented under different temperatures (950 °C, 1000 °C, 1050 °C, 1100 °C, 1150 °C) and strain rates (0.01 s−1, 0.1 s−1, 1 s−1, 10 s−1). Compared with uniaxial compression, the tensile flow stress was 29.1% higher because dynamic recrystallization softening was less sufficient in the tensile stress state. The ultimate elongation of 300M steel increased with the decrease of temperature and the increase of strain rate. To eliminate the influence of sample necking on stress-strain relationship, both the stress and the strain were calibrated using the cross-sectional area of the neck zone. A constitutive model for tensile deformation was established based on the modified Arrhenius model, in which the model parameters (n, α, Q, ln(A)) were described as a function of strain. The average deviation was 6.81 MPa (6.23%), showing good accuracy of the constitutive model.

Study on Multi-Axial Mechanical Properties of a Polyurethane Foam and Experimental Verification

2011 ◽  
Vol 311-313 ◽  
pp. 301-308
Author(s):  
Shou Hong Han ◽  
Zhen Hua Lu ◽  
Yong Jin Liu
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Polyurethane Foam ◽  
Axial Compression ◽  
Axial Loading ◽  
Hydrostatic Compression ◽  
Model Parameters ◽  
Loading Conditions ◽  
Three Point Bending ◽  
Pu Foam

In order to investigate the multi-axial mechanical properties of a kind of PU (polyurethane) foam, some experiments in different loading conditions including uni-axial tension, uni-axial compression, hydrostatic compression and three-point bending were conducted. It is shown that the hydrostatic component influences yield behavior of PU foam, the yield strength and degree of strain hardening in hydrostatic compression exceed those for uni-axial compression. In terms of the differential hardening constitutive model, the evolution of PU foam yield surface and plastic hardening laws were fitted from experimental data. A finite element method was applied to analyze the quasi-static responses of the PU foam sandwich beam subjected to three-point bending, and good agreement was observed between experimental load-displacement responses and computational predictions, which validated the multi-axial loading methods and stress-strain constitutive model parameters. Moreover, effects of two foam models applied to uni-axial loading and multi-axial loading conditions were analyzed and compared with three-point bending tests and simulations. It is found that the multi-axial constitutive model can bring more accurate prediction whose parameters are obtained from the tests above mentioned.

Sign in / Sign up

Export Citation Format

Share Document