Identification of material parameters for inelastic constitutive models: statistical analysis and design of experiments

In this paper we introduce stochastic methods to describe the influence of scattering test data on the identification of material parameters. We employ the viscoplastic constitutive model of Chan, Bodner, and Lindholm in its uniaxial form. The available test data result from three types of experiments performed at 600 °C on AINSI SS316 stainless steel, namely creep tests, constant strain rate tension tests with intermediate relaxation, and cyclic tension–compression tests. Each test has been performed with 12 specimens at different strain rates and stress rates respectively. However, for a serious statistical evaluation a larger number of experiments is required. In order to increase the number of tests we introduce stochastic simulations based on time series analysis which generate artificial data with the same stochastic behaviour as the experimental data. The method of stochastic simulation presents a widely accepted technique in engineering which does not add complexity to the process of parameter identification, but allows an investigation of the confidence in the fits of the material parameters. To keep the computation time for the identification of the material parameters as low as possible, very efficient numerical methods have to be implemented. The methods applied here for integration and nonlinear optimization are briefly introduced. The optimization strategy contains stochastic elements. Furthermore, we apply the method of statistical design of experiments to derive which combination of tests yields the most important information for an effective identification of material parameters.     

A stochastic model for parameter identification of adhesive materials

In practice, there are only a very limited number of experimental data available. Therefore, the prediction of material behaviour is difficult and a statistical analysis with a stochastic-based method is nearly impossible. In order to increase the number of tests based on experimental data, we apply the method of stochastic simulation based on time series analysis. The generated artificial data have the same stochastic behaviour as the experimental data. Advantages of artificial data are the arbitrary number of data available, and as a conclusion, the process of parameter identification can be statistically analysed. Here, we especially have experiments for adhesive materials for substantial tension tests performed at two different strain rates. Artificial data provide a stochastic proved analysis of the parameter identification concerning distribution and deviations. The analysis shows the possible range of the different material parameters and, therefore, gives a detailed view of the identification process.     

Estimation of stochastic nonlinear dynamic response of rock-fill dams with uncertain material parameters for non-stationary random seismic excitation

This research investigates the effect of uncertain material parameters on the stochastic, dynamic response of a rock-fill dam-foundation system subjected to non-stationary random excitation. The uncertain material parameter of particular interest is the shear modulus, developed from a lognormal distribution model. The stochastic seismic response model of the dam-foundation system, with uncertain material parameters and subjected to random loads is the result of a Monte Carlo simulation method. The nonlinear behavior model arises from an equivalent linear method, which considers the nonlinear variation of soil shear modulus and soil damping as a function of shear strain. Specification of the non-stationary stochastic process arises from a simulation method, which generates artificial earthquake accelerograms obtained from the product of a deterministic function of time and a stationary process. The artificial earthquake ground acceleration records reflect the characteristics of soft, medium and firm soil types. Comparison of the numerical results from these approaches provides stochasticity in earthquake seismic excitation and randomness in material parameter (shear modulus) cases. Further, the results indicate that both these cases generally influence the nonlinear dynamic response of rock-fill dams to a non-stationary seismic excitation.     

人工冻结深部软岩单轴力学性能试验及蠕变模型1）

为了了解深部软岩在冻结条件下的单轴力学性能,以东北地区的原状泥砂岩为试验对象,利用自行研制的WDT-100型人工冻土试验仪器,对其进行不同温度下的人工冻土单轴抗压强度试验和单轴蠕变试验,得到泥砂岩单轴压缩应力-应变关系曲线,各温度下试样的单轴抗压强度以及蠕变曲线.单轴压缩试验结果表明：试样在给定温度和加载速率条件下,单轴压缩应力-应变关系曲线都有较为明显的屈服点,并且都在屈服点后,强度有所提高,出现硬化现象.单轴蠕变试验结果表明：单轴压缩蠕变曲线有非线性特征,单轴压缩蠕变的等时应力-应变曲线向应变轴靠拢;单轴压缩时蠕变模量随时间的增长而降低.最后采用遗传算法优化模型参数,得出泥砂岩蠕变经验方程.与试验结果对比,发现拟合情况较好.     

A procedure to determine nonassociated constitutive equations for geomaterials

A procedure for determining a phenomenological elastic/viscoplastic nonassociated constitutive equation for geomaterials is presented. For this purpose, triaxial test data obtained with either a “true” or a classical triaxial device are necessary. The constitutive equation is aimed at describing such geomaterial properties as creep, irreversible compressibility or dilatancy, work-hardening, damage, and failure. Long-term failure can also be described with this model. According to the procedure, first the elastic parameters are determined from unloading tests (which follow short-term creep tests), then the yield function is determined, and finally the viscoplastic potential. No a priori assumption is made concerning the form of the yield function or of the viscoplastic potential; their expressions are obtained from the data by using the procedure suggested here. Examples for sand and rock salt are given. Comparisons of the model predictions with the experimental data are discussed.     

Revisit of dilation-based shock capturing for discontinuous Galerkin methods

The idea of using velocity dilation for shock capturing is revisited in this paper, combined with the discontinuous Galerkin method. The value of artificial viscosity is determined using direct dilation instead of its higher order derivatives to reduce cost and degree of difficulty in computing derivatives. Alternative methods for estimating the element size of large aspect ratio and smooth artificial viscosity are proposed to further improve robustness and accuracy of the model. Several benchmark tests are conducted, ranging from subsonic to hypersonic flows involving strong shocks. Instead of adjusting empirical parameters to achieve optimum results for each case, all tests use a constant parameter for the model with reasonable success, indicating excellent robustness of the method. The model is only limited to third-order accuracy for smooth flows. This limitation may be relaxed by using a switch or a wall function. Overall, the model is a good candidate for compressible flows with potentials of further improvement.     

ANALYSIS OF MECHANICAL CHARACTERISTICS OF FROZEN CLAY AND MODIFIED S-M CREEP MODEL1)

为合理描述人工冻结法施工的矿井土层力学特性,对某矿井土样的重塑土进行单轴抗压强度实验和单轴压缩蠕变实验,得到重塑冻结黏土在不同温度及载荷加载等级下的应力-应变曲线和蠕变曲线。实验结果表明：冻结温度越低,土样的单轴强度越大;相同冻结温度下,土样的蠕变变形随着应力水平的升高而增大。单轴压缩蠕变的等时应力-应变曲线随时间发展向应变轴靠拢;土样经历初始蠕变和等速蠕变两个阶段,在较高应力水平下有进入加速蠕变的趋势;对S-M模型中各参数的意义进行修正并考虑温度的影响,得到人工冻结黏土改进S-M蠕变显式模型,然后采用粒子群算法对人工冻结黏土S-M蠕变模型参数进行优化。改进S-M蠕变显式模型理论计算值与实验值吻合良好,表明改进S-M蠕变显式模型能较好模拟人工冻结黏土的蠕变特性。改进S-M蠕变显式模型为人工冻土蠕变计算提供一种新方法。     

A constitutive theory for creep behavior of initially isotropic materials sustaining unilateral damage

The goal of the present work is to modify structure of the creep constitutive equations existing in the literature, and simultaneously to incorporate both damage induced anisotropy and unilateral damage into the constitutive model. The proposed nonlinear-tensor constitutive equation for creep together with the damage evolution equation take into account the secondary and tertiary creep of the initially isotropic materials. The material parameters of the model are determined using basic experiments. It is shown that the creep model is capable of describing available experimental data for the lateral creep responses under uniaxial compression.     

Calibration of a simple cone-penetration model for snow

Numerical studies using the Material Point Method (MPM) have been conducted recently to model snow penetration tests for fine-grained and coarse-grained snows using small cones with diameters ranging from 2.5 mm to 4 mm, and cone half-angles between 15° and 45°. Although numerical studies have gained physical insight of these tests, due to the lengthy computation time needed for the MPM simulations, it is not feasible to use these simulations to develop a stochastic model to assess the large variations of the mechanical properties of snow typically shown in tests. In this paper, we present a simple and efficient physics-based analytical model based on equilibrium and a cavity expansion solution upon which a stochastic model is built to obtain calibrated material parameters for a Drucker–Prager (DP) model such that prediction of the model can be made. Sensitivity analysis of the analytical model indicates that cohesion and interfacial shear (friction) factor contribute significantly to the penetration hardness whereas the friction angle has little contribution. The calibrated material parameters are similar to those estimated via the MPM simulations. The quality of the stochastic model, when compared with test data, was assessed using four interval-based validation metrics with good results.     

On a damage law for creep rupture of clays with accumulated inelastic deviatoric strain as a damage measure

To avoid the dependency on origin of time, an improved damage law for creep rupture of clays is proposed considering the accumulated inelastic deviatoric strain as a measure of damage, instead of incorporating time directly. This law is incorporated into an existing anisotropic elastoplastic-viscoplastic bounding surface model for clays. The performance of the damage law was demonstrated via the simulations of creep rupture tests on undisturbed clays, and generally a good agreement between model simulations and test data was obtained. Discussions on the creep rupture parameters were followed and further improvement was suggested. At present when high quality test data for creep rupture is very limited, the proposed damage law could serve as a practical way to model creep rupture of clays.     

Constitutive relation for rheological processes: Properties of theoretic creep curves and simulation of memory decay

We study the nonlinear stress-strain constitutive relation proposed earlier for describing one-dimensional isothermal rheological processes in the case of monotonous variation of the strain (in particular, viscoplasticity, creep, relaxation, plasticity, and superplasticity). This relation contains integral time operators of the strain and strain rate, which are the norms in the Lebesgue and Sobolev spaces equipped with special weight factors, one material function, and nine material parameters determined by the results of tests of the material for relaxation, creep, long-term strength, and constant-rate strain.We analytically inverse the constitutive relation and study the properties of the inverse operator. We derive the equation of creep curves corresponding to an arbitrary law of loading at the stage of passing from the zero stress to a given constant level. We study their dependence on the material parameters and the loading stage characteristics and find restrictions on the material parameters which ensure that the asymptotic behavior of the creep curves for large times is independent of the length of the loading stage and the specific law of stress variation during this stage, i.e., we find the conditions of the model memory decay in creep. Thus we have proved that the constitutive relation proposed above can adequately model both creep and the effect of the material memory decay.     

基于爆炸切割试验的有机玻璃本构模型参数反演

为了获取爆炸切割数值模拟中有机玻璃（PMMA）的材料本构模型参数,建立了一种基于神经网络的有机玻璃Johnson Holmquist ceramics (JH-2)本构模型参数反演方法：基于从爆炸切割试验和现有研究得到的JH-2本构模型经验参数,确定本构模型参数的调整区间;使用LS-DYNA数值模拟软件对2.5 mm宽爆炸切割索切割14 mm PMMA平板过程进行数值模拟并收集平板损伤数据集;建立PMMA平板本构模型参数与损伤数据之间的神经网络模型;通过训练完成的神经网络模型对PMMA平板的JH-2本构模型参数进行反演。为验证通过反演参数的可靠性,进行了4.2 mm宽爆炸切割索切割19 mm PMMA平板试验和有限元数值模拟,计算结果中的平板损伤情况与实验结果相差较小,表明通过反演获得的JH-2本构模型参数能较好地应用于PMMA平板爆炸切割数值模拟。传统材料参数获取方法,该参数反演方法相较于可以通过较少的试验及测试,获得比较准确的材料本构模型参数。     

Evaluation of creep damage behavior of nickel-base directionally solidified superalloys with different crystallographic orientations

A crystallographic creep damage constitutive model is developed for nickel-base directionally solidified superalloys. The rates of material degradation and grain boundary void growth are considered. The governing parameters are determined from the creep test data of single crystals and directionally solidified superalloys with a crystallographic orientation. A finite element program is used to analyze the creep damage behavior of nickel-base directionally solidified superalloys for different crystallographic orientations. The results depend on the number of grains modelled and compare well with the experimental data.     

A simple endochronic transient creep model of metals with applications to variable temperature creep

Similar to the theory of endochronic plasticity, modified by Valanis in 1980, a simple endochronic transient creep model of metals is proposed by using a definition of intrinsic time ζ, measured within the creep strain tensor space, whose metric tensor is treated as a simple power form of creep strain-rate sensitive material function. The resulting constitutive equation of creep (Endocreep) contains only three material constants whose values can be determined completely by a simple creep test. An incremental form involving isothermally constant creep stress, with or without jump, and constant stress with temperature jump, are then formulated.In the applications of Endocreep on 304SS under variable temperature creep, data of simple creep tests, provided by Ohashi et al. at 650°C, Ohno et al. at 600°C, Findley and Cho at 593°C–649°C, are employed to determine material constants. The computational results in the simulation of creep tests under step-up and step-down temperature with constant axial stress are found in very good agreement with data provided by Findley and Cho. However, the results reveal that the model is too simple to deal with the recovery response of unloading. Beside this deficiency the model and its computational method proposed have a potential in the future FEM creep analysis of general thermomechanical loading history.     

A thermo-viscoelastic–viscoplastic–viscodamage constitutive model for asphaltic materials

A temperature-dependent viscodamage model is proposed and coupled to the temperature-dependent Schapery’s nonlinear viscoelasticity and the temperature-dependent Perzyna’s viscoplasticity constitutive model presented in Abu Al-Rub et al., 2009, Huang et al., in press in order to model the nonlinear constitutive behavior of asphalt mixes. The thermo-viscodamage model is formulated to be a function of temperature, total effective strain, and the damage driving force which is expressed in terms of the stress invariants of the effective stress in the undamaged configuration. This expression for the damage force allows for the distinction between the influence of compression and extension loading conditions on damage nucleation and growth. A systematic procedure for obtaining the thermo-viscodamage model parameters using creep test data at different stress levels and different temperatures is presented. The recursive-iterative and radial return algorithms are used for the numerical implementation of the nonlinear viscoelasticity and viscoplasticity models, respectively, whereas the viscodamage model is implemented using the effective (undamaged) configuration concept. Numerical algorithms are implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. The model is then calibrated and verified by comparing the model predictions with experimental data that include creep-recovery, creep, and uniaxial constant strain rate tests over a range of temperatures, stress levels, and strain rates. It is shown that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions.     

Multiaxial creep and cyclic plasticity in nickel-base superalloy C263

Physically-based constitutive equations for uniaxial creep deformation in nickel alloy C263 [Acta Mater. 50 (2002) 2917] have been generalised for multiaxial stress states using conventional von Mises type assumptions. A range of biaxial creep tests have been carried out on nickel alloy C263 in order to investigate the stress state sensitivity of creep damage evolution. The sensitivity has been quantified in C263 and embodied within the creep constitutive equations for this material. The equations have been implemented into finite element code. The resulting computed creep behaviour for a range of stress state compares well with experimental results. Creep tests have been carried out on double notched bar specimens over a range of nominal stress. The effect of the notches is to introduce multiaxial stress states local to the notches which influences creep damage evolution. Finite element models of the double notch bar specimens have been developed and used to test the ability of the model to predict correctly, or otherwise, the creep rupture lifetimes of components in which multiaxial stress states exist. Reasonable comparisons with experimental results are achieved. The γ^′ solvus temperature of C263 is about 925 °C, so that thermo-mechanical fatigue (TMF) loading in which the temperature exceeds the solvus leads to the dissolution of the γ^′ precipitate, and a resulting solution treated material. The cyclic plasticity and creep behaviour of the solution treated material is quite different to that of the material with standard heat treatment. A time-independent cyclic plasticity model with kinematic and isotropic hardening has been developed for solution treated and standard heat treated nickel-base superalloy C263. It has been combined with the physically-based creep model to provide constitutive equations for TMF in C263 over the temperature range 20–950 °C, capable of predicting deformation and life in creep cavitation-dominated TMF failure.     

The frequency response function of the creep compliance

Motivated from the need to convert time-dependent rheometry data into complex frequency response functions, this paper studies the frequency response function of the creep compliance that is coined the complex creep function. While for any physically realizable viscoelastic model the Fourier transform of the creep compliance diverges in the classical sense, the paper shows that the complex creep function, in spite of exhibiting strong singularities, it can be constructed with the calculus of generalized functions. The mathematical expressions of the real and imaginary parts of the Fourier transform of the creep compliance of simple rheological networks derived in this paper are shown to be Hilbert pairs; therefore, returning back in the time domain a causal creep compliance. The paper proceeds by showing how a measured creep compliance of any solid-like or fluid-like viscoelastic material can be decomposed into elementary functions with parameters that can be identified from best fit of experimental data. The proposed technique allows for a direct determination of the sufficient parameters needed to approximate an experimentally measured creep compliance and the presented mathematical formulae offers dependable expressions of the corresponding complex-frequency response functions.

     

Creep response of bituminous mixtures—rheological model and microstructural interpretation

The main failure mechanisms of flexible pavements, such as low-temperature cracking, fatigue failure, and rutting are strongly influenced by the viscoelastic properties of asphalt. These viscoelastic properties originate from the thermorheological behavior of bitumen, the binder material of asphalt. In this paper, the bitumen behavior is studied by means of a comprehensive experimental program, allowing the identification of viscoelastic parameters of a power-law type creep model, indicating two time scales (short-term and long-term) within the creep deformation history of bitumen. Moreover, these characteristics of the creep deformation transfer towards bitumen-inclusion mixtures, as illustrated for mastic, consisting of bitumen and filler. For this purpose, the aforementioned power-law creep model is implemented into a micromechanical framework. Finally, the activation of the different creep mechanisms as a function of the loading rate is discussed, using viscoelastic properties obtained from both static and cyclic creep tests.     

An Extension of the Monkman-Grant Model for the Prediction of the Creep Rupture Time Using Small Punch Tests

Creep tests on a small scale have the potential to be used without significant removal of material or in areas where the available material is limited. In this paper an extension of the modified Monkman-Grant model for the prediction of the creep rupture time using Small Punch Creep Tests (SPCT) is investigated. This test basically consists of punching, under constant load, a small size specimen (10×10×0.5 mm) with the ends fixed. For this purpose an AZ31B magnesium alloy, taking a test temperature of 150?ºC, has been selected. The Monkman-Grant relation is a predictive model, initially developed for uniaxial creep tests, which can be used to predict the rupture time of tests which have been interrupted once secondary stage of creep has been reached. The proposed extension of the Monkman-Grant model for SPCT is based on the definition of the Minimum Relative Punch Displacement Rate. The experimental techniques and data analysis, involving small punch testing, are explained in detail. The proposed predictive model allows the test times of small punch testing to be reduced and it can be directly applied to predict the failure time from an interrupted test at the time when the Minimum Relative Punch Displacement Rate is reached. Good correlations are obtained by comparing the failure time from the proposed Monkman-Grant extension with the experimental failure time.     

Identification of Material Damage Model Parameters: an Inverse Approach Using Digital Image Processing

A reliable prediction of ductile failure in metals is still a wide-open matter of research. Several models are available in the literature, ranging from empirical criteria, porosity-based models and continuum damage mechanics (CDM). One major issue is the accurate identification of parameters which describe material behavior. For some damage models, parameter identification is more or less straightforward, being possible to perform experiments for their evaluation. For the others, direct calibration from laboratory tests is not possible, so that the approach of inverse methods is required for a proper identification. In material model calibration, the inverse approach consists in a non-linear iterative fitting of a parameter-dependent load–displacement curve (coming from a FEM simulation) on the experimental specimen response. The test is usually a tensile test on a round-notched cylindrical bar. The present paper shows a novel inverse procedure aimed to estimate the material parameters of the Gurson–Tvergaard–Needleman (GTN) porosity-based plastic damage model by means of experimental data collected using image analysis. The use of digital image processing allows to substitute the load–displacement curve with other global quantities resulting from the measuring of specimen profile during loading. The advantage of this analysis is that more data are available for calibration thus allowing a greater level of confidence and accuracy in model parameter evaluation.