Identification of plasticity constants from orthogonal cutting and inverse analysis

The aim of this work is that from experimental determined cutting process parameters be able to predict the plasticity input constants to Finite Element Method (FEM) models. In the present study the Johnson–Cook constitutive model constants are determined on the basis of cutting process parameters in orthogonal cutting and by use of inverse analysis. Previously established links between Johnson–Cook constitutive model constants and cutting process parameters in the cutting process such as primary cutting force and chip compression ratio is used serve as a starting point in the inverse analysis. As a reference material AISI 4140 has been chosen in this study, which is a tempered steel. The Johnson–Cook constitutive model constants in the reference material are being changed within an interval of ±30%. The inverse analysis is performed using a Kalman filter. The material model for the reference material is validated on the basis of the experimental results in previous work. The model showed to predict the cutting process parameters with a high level of accuracy. The predicted Johnson–Cook constitutive model constants in the present study achieve an error between simulated- and experimental cutting process parameters of maximum 2%. The method described in this study is not limited to identify Johnson–Cook constitutive model constants, but the method can also be used for other constitutive models. The same applies to the process itself and the selected cutting process parameters, but orthogonal cutting has been used to illustrate and validate this method.     

基于卡尔曼滤波算法的功能梯度材料参数辨识

对于常用的陶瓷/金属(PSZ/NiCrAlY)功能梯度材料(FGM)的弹塑性本构参数确定问题,提出了一种改进的基于扩展卡尔曼滤波算法(EKF)的反演分析方法。该法以压痕试验中获得的荷载-压痕深度响应曲线为依据,结合有限元模拟,对材料参数进行反演辨识。反演过程中事先对实验和有限元模拟结果作逐步均化处理,以此降低系统和测量随机误差对反演结果的影响,提高问题解的收敛精度;同时,基于数值模拟结果,利用拉格朗日插值函数构建载荷-压痕深度响应面,以便插值获取任意参数组合下的响应值及其梯度值,从而提高反演的效率;另外,采用不同尺寸压头的荷载-压痕深度曲线来进一步地提高问题解的收敛性、精确性和适定性。该文从多个角度,对有效地获取FGM材料参数问题进行了详细的探讨,为材料参数的反演辨识研究提供了有益的参考。     

Identification of Gurson–Tvergaard material model parameters via Kalman filtering technique. I. Theory

In this paper quasi-static ductile fracture processes are simulated within the framework of the finite element method by means of the Gurson–Tvergaard isotropic constitutive model for progressively cavitating elastoplastic solids. The progressive degradation of the material strength properties in the fracture process zone due to micro-void growth to coalescence is modeled through the computational cell concept. Among the several model parameters to be calibrated in the computations, attention is restricted to the Tvergaard coefficients q ₁ and q ₂ and to the initial porosity f ₀ in the unstressed configuration. To identify these model parameters the inverse problem is solved via the extended Kalman filter for nonlinear systems coupled to a numerical methodology for the sensitivity analysis. In part I of this work the theory of Kalman filtering and sensitivity analysis is presented. First results concerning the identification of the Tvergaard parameters for a whole crack growth in single edge notched bend specimens made of a pressure vessel steel are presented. In order to enhance the convergence towards the final solution of the identification procedure, during the tests measurements are made of the displacements of points located in the central portion of the notched specimens, where model parameters highly affect the system state variables. In part II of this work a numerical validation of the proposed procedure in terms of uniqueness of the final identified solution, requirements of accuracy for the Bayesian initialization of the model parameters and sensitivity to the experimental measurement errors will be presented and discussed.     

Comparison of Bayesian methods on parameter identification for a viscoplastic model with damage

The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore, identification of the model parameters of the system is a topic which has attracted attention in the content of structural health monitoring. The parameters of a constitutive model are usually identified by minimization of the difference between model response and experimental data. However, the measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article, the focus is on the identification of material parameters of a viscoplastic damaging material using a stochastic simulation technique to generate artificial data which exhibit the same stochastic behavior as experimental data. It is proposed to use Bayesian inverse methods for parameter identification and therefore the model and damage parameters are identified by applying the Transitional Markov Chain Monte Carlo Method (TMCMC) and Gauss–Markov–Kalman filter (GMKF) approach. Identified parameters by using these two Bayesian approaches are compared with the true parameters in the simulation and with each other, and the efficiency of the identification methods is discussed. The aim of this study is to observe which one of the mentioned methods is more suitable and efficient to identify the model and damage parameters of a material model, as a highly non-linear model, using a limited surface displacement measurement vector and see how much information is indeed needed to estimate the parameters accurately.     

基于Sigma点全局迭代参数卡尔曼滤波的折线型本构模型参数识别

折线型本构模型控制参数少,物理意义明确,但其数学表达式复杂因而识别困难。针对折线型本构模型的参数识别,提出基于Sigma点变换的全局迭代参数卡尔曼滤波算法。所提方法以待识别参数作为状态向量,降低状态向量维度,减少计算量;基于Sigma点卡尔曼滤波避免求解雅克比(Jacobian)矩阵,实现非连续型函数本构模型的参数识别;通过设定目标函数进行全局迭代,以获得最优解。由于非线性系统下一时刻响应与历史路径有关,量测更新时由初始时刻计算到当前时刻。最后,在地震荷载下,将隔震支座系统简化为单自由度双线性模型,将桥墩简化为单自由度Takeda模型,根据该文所提出的方法理念,分别基于无迹卡尔曼滤波(unscented Kalman filter,UKF)、容积卡尔曼滤波(cubature Kalman filter,CKF)和球面单纯形径向容积正交卡尔曼滤波(spherical simplex-radial cubature quadrature Kalman filter,SSRCQKF)采样规则识别折线型本构模型参数。结果表明所提方法能够准确识别非线性参数,同时具有较强的鲁棒性,不同滤波器收敛过程及结果也有所差异。     

A Computational Inverse Technique to Determine the Dynamic Constitutive Model Parameters of Concrete

In this paper, a computational inverse technique is presented to determine the constitutive parameters of concrete based on the penetration experiments. In this method, the parameter identification problem is formulated as an inverse problem, in which the parameters of the constitutive model can be characterized through minimizing error functions of the penetration depth measured in experiments and that computed by forward solver LS-DYNA. To reduce the time for forward calculation during the inverse procedure, radial basis function approximate model is used to replace the actual computational model. In order to improve the accuracy of approximation model, a local-densifying method combined with RBF approximation model is adopted. The intergeneration projection genetic algorithm is employed as the inverse solver. Through the application of this method, the parameters of HJC constitutive model are determined. Results show that the identified constitutive parameters' computational penetration depth and projectile deceleration-time curves are closely in accordance with experimental data. The proposed inverse approach is a potentially useful tool to effectively help identify material parameters.     

Identification of Elasto-Plastic Constitutive Parameters by Self-Optimizing Inverse Method: Experimental Verifications

In this paper, the Self-Optimizing Inverse Method (Self-OPTIM) has been experimentally verified by identifying constitutive parameters solely based on prescribed boundary loadings without full-field displacements. Recently the Self-OPTIM methodology was developed as a computational inverse analysis tool that can identify parameters of nonlinear material constitutive models. However, the methodology was demonstrated only by numerically simulated testing with full-field displacement fields and prescribed boundary loadings. The Self-OPTIM is capable of identifying parameters of the chosen class of material constitutive models through minimization of an implicit objective function defined as a function of full-field stress and strain fields in the optimization process. The unique advantages of the Self-OPTIM includes: 1) model independency that is expected to open up a wide range of applications for various engineering simulations; 2) capabilities of parameter identification based solely on global measurements of boundary forces and displacements. In this paper, the Self-OPTIM inverse method is experimentally verified by using two different shapes of specimens made of AISI 1095 steel: 1) dog-bone and 2) notched specimens under a loading and unloading course. Parameters of a cyclic plasticity model with nonlinear kinematic hardening rule and associated flow theory are identified by the Self-OPTIM. Multiple tests and the inverse simulations are conducted to ensure consistent performance of the Self-OPTIM. The identified parameters are successively used to reconstruct the material response.     

An inverse method for determining elastic material properties and a material interface

A numerical procedure which integrates optimization, finite element analysis and automatic finite element mesh generation is developed for solving a two-dimensional inverse/parameter estimation problem in solid mechanics. The problem consists of determining the location and size of a circular inclusion in a finite matrix and the elastic material properties of the inclusion and the matrix. Traction and displacement boundary conditions sufficient for solving a direct problem are applied to the boundary of the domain. In addition, displacements are measured at discrete points on the part of the boundary where the tractions are prescribed. The inverse problem is solved using a modified Levenberg-Marquardt method to match the measured displacements to a finite element model solution which depends on the unknown parameters. Numerical experiments are presented to show how different factors in the problem and the solution procedure influence the accuracy of the estimated parameters.     

Characterization of a superplastic aluminium alloy ALNOVI-U through free inflation tests and inverse analysis

Numerical methods are widespread in forming applications since a deeper understanding and a finer calibration of the process can be reached without most of the assumptions used in analytical approaches. In this calibration procedure the characterization of the material behaviour is an important preliminary step that cannot be avoided. Experimental tests can be numerically modelled and material constants can be found by inverse methods making numerical results as close as possible to experimental ones. In this work material parameters of a superplastic aluminium alloy have been found by experimental forming tests and an inverse analysis. Constant pressure free inflation tests were firstly performed to find the optimal range for temperature and strain rate values. Material constants were then calculated, on the basis of these tests, minimizing errors between experimental and numerical data through a gradient based optimization iterative procedure. Constant strain rate experimental tests were finally used to refine material parameters and to gain a better agreement between experiments and numerical simulations.     

A Comparative Study of Several Material Models for Prediction of Hyperelastic Properties: Application to Silicone-Rubber and Soft Tissues

Abstract:  The correct modelling of constitutive laws is of critical importance for the analysis of mechanical behaviour of solids and structures. For example, the understanding of soft tissue mechanics, because of the nonlinear behaviour commonly displayed by the mechanical properties of such materials, makes common place the use of hyperelastic constitutive models. Hyperelastic models however, depend on sets of variables that must be obtained experimentally. In this study the authors use a computational/experimental scheme, for the study of the nonlinear mechanical behaviour of biological soft tissues under uniaxial tension. The material constants for seven different hyperelastic material models are obtained via inverse methods. The use of Martins's model to fit experimental data is presented in this paper for the first time. The search for an optimal value for each set of material parameters is performed by a Levenberg–Marquardt algorithm. As a control measure, the process is fully applied to silicone-rubber samples subjected to uniaxial tension tests. The fitting accuracy of the experimental stress–strain relation to the theoretical one, for both soft tissues and silicone-rubber (typically nonlinear) is evaluated. This study intents also to select which material models (or model types), the authors will employ in future works, for the analysis of human soft biological tissues.     

Virtual Fields Method on Planar Tension Tests for Hyperelastic Materials Characterisation

Abstract: New methods are emerging in the material characterisation field with the aim of exploiting innovative full‐field strain measurement techniques. Besides experimental issues, also numerical procedures for inverse problems should adapt to a new philosophy: the large amount of data referred to local strains should be used in an appropriate way to obtain as much benefits as possible. In this context, an experimental and numerical procedure for the characterisation of hyperelastic materials is proposed. Planar tension tests have been performed on flat rubber specimens of different geometries. Strain maps obtained by means of a 2D Digital Image Correlation system are used to implement the virtual fields method, to estimate material dependent parameters of two of the most known hyperelastic constitutive laws: Ogden and 2nd order Mooney‐Rivlin models. Numerical results and comparisons with experimental data are shown, analysing also aspects concerning implementation of the numerical procedures and computational efficiency of the algorithms.     

钢筋混凝土结构材料本构模型参数的在线识别

为保证子结构拟动力试验中数值子结构的可靠性,模型参数在线识别与更新方法逐渐受到关注。对于钢筋混凝土结构,当采用纤维模型建立数值子结构时,混凝土材料本构模型参数的选择具有较大不确定性。因此,该文提出了基于隐性卡尔曼滤波器在线识别混凝土材料本构模型参数的方法。首先,对材料本构模型参数进行分类,定义了本构参数与非本构参数,提出了约束混凝土与非约束混凝土的一致本构方程。然后,针对观测量为混凝土应力的情况进行数值仿真分析,验证了此方法的可行性。最后,通过修改OpenSees源代码,实现了此方法在观测量为构件恢复力情况下的应用。研究结果表明该文提出的方法具有较好的稳定性与较高的精度,从而在很大程度上提高了数值模型的可靠性。     

An inverse thermal–mechanical analysis of the hot torsion test for calibrating the constitutive parameters

One of the key tasks for mathematical representation of a constitutive model is calibration of its parameters. An inverse computational–experimental solution with the data modelling approach was employed here to estimate the parameters of a hyperbolic sine type constitutive equation. The solution utilizes a multi-layer constitutive model. The computational component of the inverse solution includes a rigid viscoplastic finite element code based on the thermo-mechanical coupling. The hot torsion test data comprises the experimental component of the inverse solution. Determination of the primary constitutive parameters (PCPs) pertinent to a 303 Austenitic stainless steel is presented here as an example. In order to facilitate the calibration of the sub-models, a procedure to provide an initial guess vector for the secondary constitutive parameters (SCPs) is given.     

基于鲁棒H~∞滤波的光电跟踪机动目标状态预测估计

针对光电跟踪系统中目标机动的特点和电视图像跟踪器信号处理、传输造成的测量时滞以及目标信号测量中存在的不确定干扰和噪声,选取机动目标"当前"统计模型对加速度进行建模,在所建立的光电跟踪目标加速度非零均值相关模型的基础上,采用鲁棒H∞滤波算法对光电成像识别目标运动状态进行预测估计.其预测精度比Kalman滤波提高近1倍.实验结果表明,该方法能有效地克服目标模型变化及随机噪声和干扰不确定性的影响,具有较高的预测精度和良好的鲁棒性.     

采用隐性卡尔曼滤波器的自适应子结构试验方法

在传统子结构拟动力试验基础上,提出采用隐性卡尔曼滤波器的自适应子结构试验方法,以减小由于数值子结构中相应构件的恢复力模型误差所带来的不利影响。在子结构试验过程中,在线识别试验子结构模型参数,实时更新数值子结构中相应构件的恢复力模型参数。快速准确的恢复力模型在线识别方法成为自适应拟动力子结构试验的关键,本文将试验子结构恢复力模型的模型参数作为试验子结构系统状态变量的一部分,采用隐性卡尔曼滤波器在线识别其模型参数。通过数值仿真检验采用隐性卡尔曼滤波器在线识别的自适应子结构试验方法性能。结果表明,本文所提出的自适应子结构试验方法具有很好的精度和较快的识别速度,试验结果较传统子结构试验结果有较大改善。     

紧缩场蜂窝夹层反射面板材料参数优化反求

紧缩场高精度蜂窝夹层结构反射面板由经特殊工艺处理的铝蜂窝芯和表层铝板胶接而成 , 解析计算和材料力学性能试验很难准确获得该夹层板的材料性能参数。本文中采用数值2试验混合模型方法对该种夹层板的等效材料性能参数进行了优化反求。正向分析采用有限元方法 , 逆向分析采用遗传算法和梯度法组合优化算法。正、 逆分析过程的无缝集成和组合优化算法策略使反求效率明显提高。试验验证表明 , 采用反求方法获得的材料性能参数能够精确反应该夹层板的弹性本构关系 , 建立在该材料参数基础上的有限元模型具有理想的精度。     

An inverse approach to determine the constitutive model parameters from axial crushing of thin-walled square tubes

Knowledge of the behaviour of structural components is essential for their design under crash consideration. Constitutive models describe their material behaviour in finite element (FE) codes. These constitutive models are in relation to the material parameters which have to be determined. The strain rates commonly observed in crash events are in the range of 0–500 s^-1. Classic experimental devices such as Hopkinson’s bars do not easily cover this range of strain rates. An inverse numerical approach based on the experimental quasi-static and dynamic axial crushing of thin-walled square tubes has therefore been developed to determine the constitutive model’s parameters. The inverse method is applied in this paper in two stages to determine the power type elastic–plastic constitutive model’s parameters and the Cowper–Symonds constitutive model’s parameters. The identified power law is compared with the results obtained by quasi-static tensile tests and shows that the identified parameters are intrinsic to the material behaviour. The Cowper– Symond’s parameters identified by this method are then used in FE simulation to predict the dynamic response of the same square tube subjected to bending loading. The results obtained show a good correlation between the experimental and numerical results.     

An inverse method for material parameters estimation in the inelastic range

Inverse problem theory is getting of an increasing importance in mechanical modelling as it brings a solution to the identification to rheological behaviour of materials in the nonlinear range. As a matter of fact, when using inverse identification, the problem of experimental tests interpretation associated to inhomogeneous deformation states is bypassed. This allows a more accurate material parameters determination compared to the direct identification. In this paper, an inverse identification method is proposed to determine material parameters in the nonlinear range. The algorithm developed consists of a finite element based inversion scheme associated to an optimization procedure. A sensitivity analysis is used in order to determine the gradient of the cost function, representing the difference between the measured and the calculated response, with respect to the material parameters to identify. This method is applied to the inverse identification of viscoplastic parameters entering in the constitutive function that describes the flow stress of an aluminium alloy, for large range of strain, strain rate and temperature.     

基于极限分析的三叶墙抗压强度预测模型研究

该文以极限分析法为基础,将有限元塑性极限分析下限法运用于砌体结构三叶墙的抗压强度预测。结合常见受压三叶墙破坏模式,基于材料试验和小型砌体试件试验赋予了本构模型参数。在此基础上,考虑了不均匀压应力边界条件,提出了三叶墙抗压强度预测模型。根据文献的试验数据,利用该模型预测了多个三叶墙的抗压强度,并与试验结果和抗压强度预测公式的结果进行了对比,说明了该模型的准确性。     

Determination of flow stress by inverse solution using finite element method

A newly developed method to determine flow stress of a material has been proposed. This method, named FC-method, is an application of inverse analysis. Since FC-method does not need uniformity of deformation which is the requirement for conventional methods such as uniaxial tensile or compression test, flow stress of a material expressed as a function of unknown material constants is obtained with good accuracy up to large strain range. FC-method employs, as the object function of inverse analysis, the balance of external and internal powers which are given to a material during a deformation process and spent for the deformation respectively. The external power is obtained from the load-displacement curve measured and the internal power is calculated through FEM analysis of the deformation. Then optimization of the balance through inverse analysis gives flow stress of the materia. Friction coefficient between the material and the tools for deformation is also one of the unknown constants and determined through FC-method simultaneously with flow stress. The object function of FC-method explicity contains unknown constants to be determined, therefore the cost of the analysis to obtain flow stress is reduced. Numerical study to verify FC-method was carried out using ring compression problem of type 304 stainless steel between two parallel plane dies, which clarified that FC-method was effective.