scholarly journals Identifiability of Tissue Material Parameters from Uniaxial Tests using Multi-start Optimization

2020 ◽  
Author(s):  
Babak N. Safa ◽  
Michael H. Santare ◽  
C. Ross Ethier ◽  
Dawn M. Elliott
Keyword(s):  
Experimental Data ◽  
Constitutive Model ◽  
Constitutive Models ◽  
Data Fitting ◽  
Tissue Mechanics ◽  
Lateral Strain ◽  
Model Parameters ◽  
Fiber Reinforced ◽  
Material Parameters ◽  
Tissue Material

AbstractDetermining tissue biomechanical material properties from mechanical test data is frequently required in a variety of applications, e.g. tissue engineering. However, the validity of the resulting constitutive model parameters is the subject of debate in the field. Common methods to perform fitting, such as nonlinear least-squares, are known to be subject to several limitations, most notably the uniqueness of the fitting results. Parameter optimization in tissue mechanics often comes down to the “identifiability” or “uniqueness” of constitutive model parameters; however, despite advances in formulating complex constitutive relations and many classic and creative curve-fitting approaches, there is no accessible framework to study the identifiability of tissue material parameters. Our objective was to assess the identifiability of material parameters for established constitutive models of fiber-reinforced soft tissues, biomaterials, and tissue-engineered constructs. To do so, we generated synthetic experimental data by simulating uniaxial tension and compression tests, commonly used in biomechanics. We considered tendon and sclera as example tissues, using constitutive models that describe these fiber-reinforced tissues. We demonstrated that not all of the model parameters of these constitutive models were identifiable from uniaxial mechanical tests, despite achieving virtually identical fits to the stress-stretch response. We further show that when the lateral strain was considered as an additional fitting criterion, more parameters are identifiable, but some remain unidentified. This work provides a practical approach for addressing parameter identifiability in tissue mechanics.Statement of SignificanceData fitting is a powerful technique commonly used to extract tissue material parameters from experimental data, and which thus has applications in tissue biomechanics and engineering. However, the problem of “uniqueness” or “identifiability” of the fit parameters is a significant issue, limiting the fit results’ validity. Here we provide a novel method to evaluate data fitting and assess the uniqueness of results in the tissue mechanics constitutive models. Our results indicate that the uniaxial stress-stretch experimental data are not adequate to identify all the tissue material parameters. This study is of potential interest to a wide range of readers because of its application for the characterization of other engineering materials, while addressing the problem of uniqueness of the fitted results.

A Cyclic Plasticity Modeling for Uniaxial and Multiaxial Ratcheting Simulation of Austenitic Steel

2012 ◽  
Author(s):  
Salim Meziani ◽  
Lynda Djimli
Keyword(s):  
Experimental Data ◽  
Stainless Steel ◽  
Constitutive Model ◽  
Data Base ◽  
Good Choice ◽  
Cyclic Plasticity ◽  
Strain History ◽  
Material Parameters ◽  
Plastic Shakedown

The first objective of this paper investigates the influence of the previous strain history on ratcheting of the 304 L stainless steel on ambient temperature. The identification is done using the Chaboche constitutive model. New tests were performed where different strain-controlled histories have been applied prior to ratcheting tests. It is demonstrated that under the same conditions, one can observe ratcheting, plastic shakedown or elasticity according to the prior strain-controlled history. The second objective points out the correlation between the experimental data base devoted to the identification of the material parameters and the quality of the predictions in cyclic plasticity. The results suggest that the choice of the tests should be closely linked to the capabilities of the model. In particular, the presence of non proportional strain-controlled tests in the data base may be not a good choice if the model itself is not able to represent explicitly such a character.

scholarly journals Identification of orthotropic material parameters for acute, necrotic, fibrotic and remodelling myocardial infarcts in the rat

2019 ◽  
Author(s):  
Mazin S. Sirry ◽  
Laura Dubuis ◽  
Neil H. Davies ◽  
Jun Liao ◽  
Thomas Franz
Keyword(s):  
Constitutive Model ◽  
Orthotropic Material ◽  
Constitutive Models ◽  
Biaxial Stress ◽  
Percentage Error ◽  
Fe Model ◽  
Stress Strain ◽  
Material Parameters ◽  
Strain Data ◽  
Tensile Experiment

AbstractFinite element (FE) models have been effectively utilized in studying biomechanical aspects of myocardial infarction (MI). Although the rat is a widely used animal model for MI, there is a lack of material parameters based on anisotropic constitutive models for rat myocardial infarcts in literature. This study aimed at employing inverse methods to identify the parameters of an orthotropic constitutive model for myocardial infarcts in the acute, necrotic, fibrotic and remodelling phases utilizing the biaxial mechanical data developed in a previous study. FE model was developed mimicking the setup of the biaxial tensile experiment. The orthotropic case of the generalized Fung constitutive model was utilized to model the material properties of the infarct. The parameters of Fung model were optimized so that the FE solution best fitted the biaxial experimental stress-strain data. A genetic algorithm was used to minimize the objective function. Fung orthotropic material parameters for different infarct stages were identified. The FE model predictions best approximated the experimental data of the 28 days infarct stage with 3.0% mean absolute percentage error. The worst approximation was for the 7 days stage with 3.6% error. This study demonstrated that the experimental biaxial stress-strain data of healing rat infarcts could be successfully approximated using inverse FE methods and genetic algorithms. The material parameters identified in this study will provide an essential platform for FE investigations of biomechanical aspects of MI and the development of therapies.

Measurement and Calibration of the Parameters of Hypoplasticity Model for an Iraqi Soil

2020 ◽  
Vol 857 ◽  
pp. 243-252
Author(s):  
Aysar Hassan Subair ◽  
Ala Nasir Aljorany
Keyword(s):  
Constitutive Model ◽  
Void Ratio ◽  
Initial Stresses ◽  
Model Parameters ◽  
State Variables ◽  
Soil Behavior ◽  
Dense Sand ◽  
Hypoplastic Model ◽  
Material Parameters ◽  
Wide Range

There are many constitutive models that have been used to model the mechanical behavior of soils. Some of these models are either unable to represent important features such as the strain softening of dense sand or required many parameters that can be hard to obtain by standard laboratory tests. Because of that, a more reliable constitutive model, which is capable to capture the main features of the soil behavior with easily obtained parameters, is required. The Hypoplasticity model is considered as a promising constitutive model in this respect. It is considered as a particular class of rate non-linear constitutive model at which the stress increment is expressed in a tensorial equation as a function of strain increment, actual stress, and void ratio. The hypoplastic model required only eight material parameters (critical friction angle critical, maximum and minimum void ratio respectively), granular stiffness hs and the model constants n, α, β). The appealing feature of the hypoplastic model is that the material parameters are separated from the state variables (void ratio and the initial stresses). This feature enables the model to simulate the soil behavior under a wide range of stresses and densities with the same set of material parameters. In this research, a brief description of the Hypoplasticity model is presented. Detailed discussions regarding the measurement and calibration of the model parameters of an Iraqi soil are then exposed. It is concluded that only Consolidated Drained (CD) triaxial test, oedometer test, and the well-known limit density tests are needed to get all the parameters of the hypoplasticity model.

Viscoelastic Characterization of Fiber-Reinforced Elastomeric Composites at Finite Strain

2010 ◽  
Vol 123-125 ◽  
pp. 603-606
Author(s):  
Mohammad Tahaye Abadi
Keyword(s):  
Constitutive Model ◽  
Large Deformation ◽  
Finite Strain ◽  
Mechanical Response ◽  
Viscoelastic Model ◽  
Constitutive Law ◽  
Micromechanical Modeling ◽  
Fiber Reinforced ◽  
Material Parameters ◽  
Elastomeric Composites

A viscoelastic model is developed to describe the mechanical response of fiber-reinforced elastomeric composites at large deformation. A continuum approach is used to model the macroscopic mechanical behavior of elastomeric materials reinforced with unidirectional fibers, in which the resin and fibers are regarded as a single homogenized anisotropic material. The anisotropic viscoelastic constitutive model is developed considering transient reversible network theory. An efficient computational algorithm based on micromechanical modeling is proposed to relate the material parameters of constitutive model to the mechanical properties of composite constituents at finite strain. The microstructure is identified by a representative volume element (RVE) and it is subjected to large deformation with considering the conformity of opposite boundaries. The material parameters of the viscoelastic constitutive law are determined based on the response of heterogeneous microstructure which is examined under different loading conditions.

State of the Art of Constitutive Model of Concrete Materials Based on Damage Mechanics

2011 ◽  
Vol 194-196 ◽  
pp. 848-852
Author(s):  
Duo Xin Zhang ◽  
Qing Yun Wang
Keyword(s):  
Constitutive Model ◽  
Damage Mechanics ◽  
State Of The Art ◽  
Constitutive Models ◽  
Experimental Tests ◽  
Constitutive Relationship ◽  
Model Parameters ◽  
Softening Effect ◽  
Volumetric Expansion ◽  
Concrete Materials

This study centered on the development of constitutive model of the material based on damage mechanics. Volumetric expansion, unilateral behavior and softening effect have been pointed out as three difficulties during setting constitutive model of concrete, the applicable and deficiency of the existed constitutive relationship been reviewed, and the methods used to deal above difficulties were overviewed, Meanwhile, the background of existed model has been summarized and listed systematically. The development of a thermodynamic approach to constitutive model of concrete, with emphasis on the rigorous and consistency both in the formulation of constitutive models and in the identification of model parameters based on experimental tests has been potential direction of the future study, and hoped furnished basement for the elastic to plastic coupled damage mechanics constitutive model of concrete.

Evolution of Anand Parameters With Elevated Temperature Aging for SAC Leadfree Alloys

2020 ◽  
Author(s):  
Pradeep Lall ◽  
Vikas Yadav ◽  
Jeff Suhling ◽  
David Locker
Keyword(s):  
Experimental Data ◽  
High Strain ◽  
Constitutive Models ◽  
Tensile Tests ◽  
Model Parameters ◽  
Strain Rates ◽  
Automotive Electronics ◽  
High Strain Rates ◽  
Operating Temperatures ◽  
Electronic Assemblies

Abstract Electronic equipment in automotive, agricultural and avionics applications may be subjected to temperatures in the range of −55 to 200°C during storage, operation and handling in addition to high strain-rates. Strain rates in owing to vibration and shock may range from 1–100 per sec. Temperature in electronic assemblies depends typically on location, energy dissipation and thermal architecture. Some investigators have indicated that the required operating temperature is between −40 to 200°C for automotive electronics located underhood, on engine, on transmission. Prior data indicates the evolution of mechanical properties under extended exposures to high temperatures. However, the constitutive models are often only available for pristine materials only. In this paper, effect of low operating temperatures (−65°C to 0°C) on Anand-model parameters at high strain rates (10–75 per sec) for aged SAC (SAC105 and SAC-Q) solder alloys has been studied. Stress-Strain curves have been obtained at low operating temperatures using tensile tests. The SAC leadfree solder samples were subjected to isothermal-aged up to 4-months at 50°C before testing. Anand Viscoplastic model has been used to describe the material constitutive behavior. Evolution of Anand Model parameters for SAC solder has been investigated. The computed parameters of the experimental data were used to simulate the tensile test and verified the accuracy of the model. A good correlation was found between experimental data and Anand predicted data.

Numerical Studies of the Effect of Constitutive Model Parameters as Reflecting Polymer Molecular Structure on Extrudate Swell

2002 ◽  
Vol 12 (5) ◽  
pp. 252-259 ◽  
Author(s):  
Nattapong Nithi-Uthai ◽  
Ica Manas-Zloczower
Keyword(s):  
Molecular Weight ◽  
Constitutive Model ◽  
Full Range ◽  
Constitutive Models ◽  
Model Parameters ◽  
Extrudate Swell ◽  
Relaxation Spectra ◽  
Shear Rates ◽  
Swell Ratio ◽  
Numerical Predictions

Abstract PolyFlow, a software package based on the finite element method was employed to simulate the extrudate swell for polybutadiene of various molecular weight (Mw) and molecular weight distribution (MWD). We calculated the relaxation spectra for the different samples and then inserted the spectra into a standard K-BKZ constitutive model used in the numerical simulations. Accurate predictions of MWD confirm the completeness of frequency range in the oscillatory shear experimental data. In turn, the wholeness of relaxation spectra as substantiated by MWD predictions, sustain the level of confidence when using constitutive models based on these spectra. We demonstrate the importance of using the full range of relaxation spectrum rather than a short range around typical shear rates for the accuracy of the numerical predictions. We found extrudate swell ratio (ESR) to be strongly dependent on MWD and stress conditions at the die exit.

Bodner-Partom Constitutive Model and Nonlinear Finite Element Analysis

1990 ◽  
Vol 112 (3) ◽  
pp. 287-291 ◽  
Author(s):  
F. A. Kolkailah ◽  
A. J. McPhate
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Plastic Strain ◽  
Constitutive Model ◽  
Finite Element Model ◽  
Numerical Technique ◽  
Element Model ◽  
Material Behavior ◽  
Model Parameters ◽  
Elastic Plastic

In this paper, results from an elastic-plastic finite-element model incorporating the Bodner-Partom model of nonlinear time-dependent material behavior are presented. The parameters in the constitutive model are computed from a leastsquare fit to experimental data obtained from uniaxial stress-strain and creep tests at 650°C. The finite element model of a double-notched specimen is employed to determine the value of the elastic-plastic strain and is compared to experimental data. The constitutive model parameters evaluated in this paper are found to be in good agreement with those obtained by the other investigators. However, the parameters determined by the numerical technique tend to give response that agree with the data better than do graphically determined parameters previously used. The calculated elastic-plastic strain from the model agreed well with the experimental strain.

scholarly journals Numerical Analysis of Test Embankment on Soft Ground Using Multi-Laminate Type Model with Destructuration / Analiza Numeryczna Nasypu Drogowego Posadowionego Na Gruncie Słabonosnym Z Zastosowaniem Modelu Wielopłaszczyznowego Z Destrukturyzacja

2011 ◽  
Vol 57 (1) ◽  
pp. 27-44
Author(s):  
M. Cundi
Keyword(s):  
Constitutive Model ◽  
Constitutive Models ◽  
In Situ Stress ◽  
Type Model ◽  
Model Parameters ◽  
Structural Anisotropy ◽  
Soft Clays ◽  
Stress Induced Anisotropy ◽  
Test Embankment

Abstract A multi-laminate constitutive model for soft soils incorporating structural anisotropy is presented. Stress induced anisotropy of strength, which is present in multi-laminate type constitutive models, is augmented by directionally distributed overconsolidation. The model is presented in the elastic-plastic version in order to simulate strength anisotropy of soft clayey soils and destructuration effects. Performance of the model is shown for some element tests and for the numerical simulation of a trial road embankment constructed on soft clays at Haarajoki, Finland. The numerical calculations are completed with the commercial finite element code capable to perform coupled static/consolidation analysis of soils. Problems related to the initiation of in situ stress state, conditions of preconsolidation, as well as difficulties linked to estimation of the model parameters are discussed. Despite simple assumptions concerning field conditions and non-viscous formulation of the constitutive model, the obtained final results are of a sufficient accuracy for geotechnical practice.

An Efficient Method for the Optimization of Viscoplastic Constitutive Model Constants

2010 ◽  
Author(s):  
James P. DeMarco ◽  
Erik A. Hogan ◽  
Calvin M. Stewart ◽  
Ali P. Gordon
Keyword(s):  
Constitutive Model ◽  
Random Noise ◽  
Constitutive Models ◽  
Optimization Method ◽  
Complex Stress ◽  
Operating Conditions ◽  
Widespread Application ◽  
Material Constants ◽  
Material Parameters ◽  
Critical Components

Constitutive modeling has proven useful in providing accurate predictions of material response in components subjected to a variety of operating conditions; however, the high number of experiments necessary to determine appropriate constants for a model can be prohibitive, especially for more expensive materials. Generally, up to twenty experiments simulating a range of conditions are needed to identify the material parameters for a model. In this paper, an automated process for optimizing the material constants of the Miller constitutive model for uniaxial modeling is introduced. The use of more complex stress, strain, and temperature histories than are traditionally used allows for the effects of all material parameters to be captured using significantly fewer tests. A graphical user interface known as uSHARP was created to implement the resulting method, which determines the material constants of a viscoplastic model using a minimum amount of experimental data. By carrying out successive finite element simulations and comparing the results to simulated experimental test data, both with and without random noise, the material constants were determined from 75% fewer experiments. The optimization method introduced here reduces the cost and time necessary to determine constitutive model constants through experimentation. Thus it allows for a more widespread application of advanced constitutive models in industry and for better life prediction modeling of critical components in high-temperature applications.

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