Identification of Gurson's material constants by using Kalman filter

A new approach based on the inverse analysis is proposed for estimating material parameters of nonlinear constitutive equations. Using the measurable response of experimental specimens, an inverse analysis is carried out to predict most suitable values of unknown material constants. In general, the accuracy of prediction depends on geometries of specimens and types of measurements. In order to identify optimal experimental procedure, the Kalman filter technique is employed. We have chosen the Gurson model for porous elastic-plastic materials as the material model and its two parameters as the unknown constants. Gurson's constitutive model has been widely used for studying ductile fracture as well as shear localization of various metals. Detailed finite element simulations are performed to demonstrate the effectiveness of the proposed method in determination of the two parameters relating to void nucleation. In the Kalman filter procedure, it is found that the rate of convergence to the correct solutions depends on shapes of test specimens, initial estimates of the unknown parameters, and accuracy of measured data as well as computed reference data. Our analysis predicts that when two differently shaped specimens under tension are used (i.e., a plate with a center hole and another with double side notches), a significant improvement occurs in the rate of convergence.     

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.     

Back analysis of model parameters in geotechnical engineering by means of soft computing

In this paper, a parameter identification (PI) method for determination of unknown model parameters in geotechnical engineering is proposed. It is based on measurement data provided by the construction site. Model parameters for finite element (FE) analyses are identified such that the results of these calculations agree with the available measurement data as well as possible. For determination of the unknown model parameters, use of an artificial neural network (ANN) is proposed. The network is trained to approximate the results of FE simulations. A genetic algorithm (GA) uses the trained ANN to provide an estimate of optimal model parameters which, finally, has to be assessed by an additional FE analysis. The presented mode of PI renders back analysis of model parameters feasible even for large‐scale models as used in geotechnical engineering. The advantages of theoretical developments concerning both the structure and the training of the ANN are illustrated by the identification of material properties from experimental data. Finally, the performance of the proposed PI method is demonstrated by two problems taken from geotechnical engineering. The impact of back analysis on the actual construction process is outlined. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

聚氨酯隔振器特性的有限元分析

利用不同的本构模型对聚氨酯材料的实际应力－应变曲线进行拟合,运用ABAQUS软件的超弹性材料评估功能,得出了适合聚氨酯材料的最佳本构模型。基于该本构模型,对一种新型聚氨酯隔振器的静、动态性能进行有限元分析,得到了隔振器的主要性能指标。通过隔振器的试验,验证了有限元分析的有效性,对聚氨酯材料在新型隔振元件设计中的应用具有一定的指导意义。     

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.     

An inverse optimal control problem in the electrical discharge machining

Electrical discharge machining (EDM) is a thermal material removal process by means of electrical discharge. Because of the stochastic nature of the EDM process, electro-thermal energy conversion in the discharge zone is still not well understood. In this paper, an inverse optimal control problem was used for analysis and optimization of energy conversion processes in order to improve machining efficiency. Modeling and identification of a thermal process were conducted using the inverse heat transfer problem based on the known temperature within a workpiece. In addition to the temperature field, this approach allows the determination of unknown heat flux density distribution on the workpiece surface. By using the heat flux, the inverse optimal control problem based on minimizing a Tikhonov functional allows to obtain the optimal heat source parameters (discharge power and discharge duration) on the discharge energy. In this context, the concept of inverse problem allows reliable determination of the optimal discharge energy to achieve the highest possible productivity with the desired quality. The performance of prediction of the heat affected zone compared to the experimental results showed a good agreement, which confirms the validity of the inverse method compared to the reported models.     

INELASTIC CONSTITUTIVE PARAMETER IDENTIFICATION USING AN EVOLUTIONARY ALGORITHM WITH CONTINUOUS INDIVIDUALS

This paper presents a method for identifying the parameter set of inelastic constitutive equations, which is based on an evolutionary algorithm proposed by the authors. The advantage of the method is that appropriate parameters can be identified even when the measured data are subject to considerable errors and the model equations are inaccurate. The design of experiments suited for the parameter identification of a material model by Chaboche under the uniaxial loading and stationary temperature conditions was first considered. Then the parameter set of the model was identified by the proposed method from a set of experimental data. In comparison to those by other methods, the resultant stress–strain curves by the proposed method correlated well and reliably to the actual material behaviors. © 1997 by John Wiley & Sons, Ltd.     

Nonlinear material parameter estimation for characterizing hyper elastic large strain models

An automated, systematic, and computationally efficient methodology to estimate the material parameters for characterizing general nonlinear material models for large strain analysis (e.g., hyperelastic and hyper foam materials) is presented. Such constitutive material models often require a large number of material constants to describe a host of physical phenomena and complicated deformation mechanisms. Extracting such material constants for a model from the volumes of data generated in the test laboratory is usually a very difficult, and frustrating. The integrated code COMPARE (that is an acronym of Constitutive Material PARameter Estimator) is being developed to enable the determination of an “optimum” set material parameters by minimizing the errors between the experimental test data and the predicted response. The key ingredients of COMPARE are listed as follows: (i) primal analysis tools (response functionals) for differential form of constitutive models; (ii) sensitivity analysis; (iii) optimization technique of an error/cost function; and (iv) graphical user interface. The code COMPARE casts the estimation of the material parameters as a minimum-error, weighted-multiobjective, optimization problem. Detailed derivations and results generated by applying the proposed technique to a comprehensive set of test data are given. These results have clearly demonstrated the great practical utility of the automated scheme developed. Received 17 September 1999     

Assessment of different ductile damage models and experimental validation

The tough fuel economy and emissions standards facing automotive industry creates the need for lightweight construction and the use of new generation of materials. However, the use of non-conventional materials leads to difficulties in the prediction of material behaviour during sheet metal forming processes, including damage and formability limits, thus challenging the numerical simulation. This paper seeks to contribute in the prediction of fracture on sheet metal alloys. Three constitutive damage models are used, GTN, Johnson Cook and Lemaitre, to simulate, as realistically as possible, the mechanical behaviour of the sheet metal material. The corresponding parameters of damage models are identified using an inverse analysis procedure, based on experimental test data. Finally, to validate and verify the applicability of the studied damage models to predict fracture, experiments are compared with FE simulations.     

Experimental investigation on constitutive behavior of PVB under impact loading

During automotive related accidents, PVB plays an important role in both pedestrian and passenger protection as an interlayer of automotive windshield. In this paper, dynamic constitutive behavior of PVB material is thoroughly studied. Firstly, a set of dynamic compression impact experiments on PVB specimens using SHPB (Split Hopkinson Pressure Bar) method are conducted at strain rates from 700/s to 4500/s. Details of the constitutive response is analyzed based on the validation of experiment data. Stress-strain curve of PVB is then divided into two parts, i.e., “Compaction Stage” and “Hardening Stage”. Dislocations and entanglements among molecules are major reasons for the two-stage phenomena. Constitutive behaviors are different in low and high speed impacts, leading to three times more energy absorption ability of PVB in high speed impact scenario. Further, data fitting models based on both Mooney–Rivlin and Ogden Model are studied and then compared. Mooney–Rivlin Model is found to be more appropriate to describe PVB material. Moreover, PVB is proved to be a rate-dependent material with the failure strength intensify factor β ≈ 4. PVB material shows little viscoelasticity after comparison of the both models with and without the viscoelasticity part. Results offer critical experimental data, constitutive models and analysis of PVB material to further study of automotive crashworthiness and pedestrian/passenger protection.     

Problems of identification of mechanical characteristics of viscoelastic composites

Summary The problem of modelling and identification of viscoelastic properties of composites as asphalt concrete, based on experimental investigations is the subject of this paper. Only viscoelastic properties of such materials are taken into consideration and usefulness of linear constitutive relations in differential form is examined. The identification problem is formulated in terms of sensitivity analysis and optimization theory. An approach to select the best from the considered class of material models is proposed and the values of associated material parameters are determined by minimization of objective function representing a measure of a difference between theoretically calculated and experimentally obtained response of a sample to sinusoidal loading. Obtained this way, results are compared with those calculated using the method based on the approach proposed by Bland and Lee [1] for calculation material parameters of Burgers model. It has been shown that differential constitutive relations with constant coefficients have very restricted application in the considered case because they are in force in narrow domains of excitation frequency. The application of models with frequency-dependent coefficients is one of the possible solutions of this problem [2]. Another approach can also be proposed based on the application of fractional calculus in viscoelasticity, see Bagley and Torvik [3].     

Void growth simulations in single crystals

The growth and coalescence of microvoids leading to ductile failure in single crystals is simulated using the finite element method. Finite deformation, rate dependent, crystal plasticity theory is used in the context of 2D plane strain models. The details of material failure at the microscale and macroscale are investigated under variation in a range of parameters including void volume fraction, loading state and lattice structure and orientation. Remeshing is used to improve accuracy of results. Results are compared with those produced by models based on other constitutive theories and experimental observation.     

DoGeNetS: using optimisation to discriminate regulatory network topologies based on gene expression data

Gene regulatory networks (GRNs) determine the dynamics of gene expression. Interest often focuses on the topological structure of a GRN while numerical parameters (e.g. decay rates) are unknown and less important. For larger GRNs, inference of structure from gene expression data is prohibitively difficult. Models are often proposed based on integrative interpretation of multiple sources of information. We have developed DoGeNetS (Discrimination of Gene Network Structures), a method to directly assess candidate models of GRN structure against a target gene expression data set. The transsys language serves to model GRN structures. Numeric parameters are optimised to approximate the target data. Multiple restarts of optimisation yield score sets that provide a basis to statistically discriminate candidate models according to their potential to explain the target data. We demonstrate discrimination power of the DoGeNetS method by relating structural divergence to divergence between gene expression data sets. Known models are used to generate target expression data, and a set of candidate models with a defined structural divergence to the true model is produced. Structural divergence and divergence of expression profiles after optimisation are strongly correlated. We further show that discrimination is possible at noise levels exceeding those typical of contemporary microarray data. DoGeNetS is capable of discriminating the best GRN structure from among a small number of candidates. p values indicate whether differences in divergence of expression are significant. Although this study uses single gene knockouts, the DoGeNetS method can be adapted to simulate a virtually unlimited range of experimental conditions. [Includes supplementary material].     

正交异性膜材大变形行为的有限质点法求解

建筑薄膜具有正交异性和拉伸非线性的力学特性,其本构关系的表征和大变形行为的描述都较为复杂,具有很强的几何、材料双重非线性特征。有限质点法是一种新颖的结构数值分析方法,它将传统分析力学方法中复杂的函数连续体模型用清晰的离散质点物理模型取代,通过质点的运动描述结构的行为。该文根据途径单元的基本概念直接在质点内力计算过程中引入不同的膜材本构,将有限质点法拓展应用于正交异性薄膜结构的几何与材料非线性大变形分析。为了准确表征膜材力学特性,根据复合材料本构理论分别建立了适用于有限质点法的正交异性膜材的线性与非线性拉伸本构模型,并通过若干算例探讨了该文方法和程序的适用性和正确性。     

Parameter Identification Method of Large Macro-Micro Coupled Constitutive Models Based on Identifiability Analysis

Large and complex macro-micro coupled constitutive models, which describe metal flow and microstructure evolution during metal forming, are sometimes overparameterized with respect to given sets of experimental datum. This results in poorly identifiable or non-identifiable model parameters. In this paper, a systemic parameter identification method for the large macro-micro coupled constitutive models is proposed. This method is based on the global and local identifiability analysis, in which two identifiability measures are adopted. The first measure accounts for the sensitivity of model results with respect to single parameters, and the second measure accounts for the degree of near-linear dependence of sensitivity functions of parameter subsets. The global identifiability analysis adopts a sampling strategy with only a limited number of model evaluations, and the strategy is a combination of Latin-hypercube sampling, one-factor-at-a-time sampling and elitism preservation strategy. The global identifiability index is the integration of the corresponding local index. A hybrid global optimization method is designed to identify the parameter. Firstly, the genetic algorithm is adopted to identify the model parameter rudely, and then the obtained parameter is further refined through the improved Levenberg-Marquardt algorithm. The niching method is used to maintain the population diversity and to choose the initial value for the Levenberg-Marquardt algorithm. A transition criterion between the genetic algorithm and the Levenberg-Marquardt algorithm is proposed, through the improvement on the average objective function value of the chromosomes and the objective function value of the best chromosome. During optimization by the Levenberg-Marquardt algorithm, the local identifiability analysis is taken at the beginning stage of each iteration, and then the variable with poor identifiability remains unchanged in this iteration; the problem of violation constraint for some solution is solved through adjusting the search step length. At last, taking Ti-6Al-4V as an example, a set of satisfactory material parameters is obtained. The calculated results agree with the experimental results well. The identified results show that some parameters involved in the model are poorly identifiable; at the same time, the identifiability analysis method can provide a guide to experiment design.     

ANALYZING DUCTILE FRACTURE USING DUAL DILATIONAL CONSTITUTIVE EQUATIONS

Abstract— By adopting a suggestion made by Thomason, a new failure criterion for the Gurson-Tvergaard model has been recently introduced by the authors. In this study, a method based on the Gurson-Tvergaard constitutive model and the new failure criterion is applied to the analysis of ductile fracture. The main features of the method are that the material failure is a natural process of the development of Thomason's dual dilational constitutive responses, and the void volume fraction corresponding to the failure by void coalescence is not necessarily a material constant and is not needed to be fitted beforehand. Furthermore, void nucleation parameter(s) can be numerically fitted from experimental tension results. This method has been implemented into the ABAQUS finite element program via a user material subroutine and is applied to the prediction of tension problems conducted by the authors. In the analyses, two strain-controlled void nucleation models have been studied and compared. The void nucleation parameters corresponding to the two models have been calibrated. The crack initiation of both smooth and notched axisymmetric tensile specimens are well predicted by the method. Finally, several critical issues in the analysis of ductile fracture are discussed.     

Generalised constitutive equations for densification of metal matrix coated fibre composites

Abstract

The present paper completes a study of constitutive equations for the consolidation processing of continuous fibre reinforced metal matrix composite materials. It builds on an earlier paper in which physically based constitutive equations were derived for the case of symmetrical, isostatic loading. In the present paper, constitutive equations are developed for in plane, general stress states. The total deformation of the consolidating composite is expressed as the sum of a conventional deviatoric creep term, together with a dilatational term, which was derived using a variational method previously published. The equations contain only two material parameters, which are the conventional creep coefficient and exponent for the fibre coating material (in this case, Ti-6Al-4V). The resulting equations have been implemented into finite element software enabling the simulation of practical consolidation processes. The model has been verified by comparing predicted results with those obtained from independent micromechanical models. A number of experimental tests have been carried out, and the model is used to predict the rates of densification for a range of experimental pressure and temperature histories. Good comparisons have been achieved.     

Modeling short- and long-term time-dependent nonlinear behavior of polyethylene

A new methodology for developing macromechanical constitutive formulations for time-dependent materials is presented in this article. In particular, two phenomenological constitutive models for polymer materials are illustrated, describing time-dependent and nonlinear mechanical behavior. In this new approach, short-term creep test data are used for modeling both short-term and long-term responses. The differential form of a model is used to simulate typical nonlinear viscoelastic polymeric behavior using a combination of springs and dashpots. Unified plasticity theory is then used to develop the second model, which is a nonlinear viscoplastic one. Least squares fitting is applied for the determination of material parameters for both models, based on experimental results. Due to practical constraints, experimental data are usually available for short-term time-frames. In the presented proposed formulation, the material parameters determined from short-term testing are used to obtain material parameter relationships for predicting the long-term material response. This is done by extending short-term information for longer time frames. Finally, theoretical and experimental results of tensile tests on polyethylene subjected to various load levels and test times are compared and discussed. Very good agreement of the modeling results with experimental data shows that the developed formulation provides a flexible and reliable framework for predicting load responses of polymers.     

Some Experiences with a Nonlinear Experimental Design Criterion

The optimal experimental designs for estimating the parameters in certain nonlinear models in various situations are given, and it is noted that these designs usually consist of suitable replicates of a small set of experiments, the number of which is equal to the number of unknown parameters. In view of the computational difficulty in obtaining the optimal experimental designs, it is suggested that the experience gained with these examples be regarded as typical, and on this basis computational “short cuts” to the optimal (or at least near optimal) designs are available. Also discussed is a grave disadvantage of replicated optimal designs, namely that such experimentation is of little use in highlighting inadequacies of the assumed model, if any exist.