Material Parameters Of Constitutive Model Research Articles

Automatic parameter identification of a shape memory alloy model using characteristic experimental data points

Identifying material parameters of constitutive models can be a time consuming process. This is especially evident when the constitutive models have many parameters. In this work, an automatic identification procedure is described to determine the various parameters of a shape memory alloy model. The procedure requires some parameters as manual inputs (to be determined via trial and error) and determines some of the parameters directly from experimental data. In addition, the procedure calculates some of the parameters using Newton’s method based on characteristic data points so that the simulation curves pass through those points. As a result, the method essentially decouples the effects of the parameters on the simulation uniaxial test curves. The automatic identification procedure is applied for uniaxial tests dealing with transformation, tension–compression asymmetry, internal loops, plasticity and functional fatigue. The procedure is fast, flexible and reasonably accurate. However, the approach is currently limited to uniaxial tests, small strains and needs to be tailored to each model individually.

Determination of material parameters in constitutive models using adaptive neural network machine learning

A challenge in the constitutive modeling of time dependent, non-linear solids is the identification of potentially large numbers of material parameters. Here we present an efficient method to determine these parameters using a machine learning algorithm based on Singular Value Decomposition (SVD) and an adaptive neural network (NN). SVD compresses training data and provides outputs for the NN. The trained network rapidly computes the material responses for a large set of material parameters. These responses are then compared with experimental data to determine the optimal parameters. We test our algorithm by performing uniaxial cyclic and relaxation tests on three hydrogels with very different time dependent behaviors: a chemically and physically crosslinked polyampholyte (c-PA) gel; a pure physically crosslinked PA (p-PA) gel, and a Poly(vinylalcohol) (PVA) hydrogel with both chemical and physical crosslinks.

Machine learning-assisted parameter identification for constitutive models based on concatenated loading path sequences

A hybrid strategy for the identification of material parameters of constitutive models is presented. One main challenge in the context of classic optimisation-based parameter identification schemes is the generation of adequate starting values for the multi-objective optimisation procedure. We address this issue by employing an artificial neural network that is trained with data obtained from the material model, more precisely speaking, from different solutions of the direct problem for homogeneous states of deformation. As a result, a solution of the inverse problem of parameter identification can be approximated with the help of a neural network processing experimental data. This approximate solution is used as a starting value for a subsequent, classic optimisation-based parameter identification approach. One key advantage of this strategy is that a network only has to be trained once per material model and can subsequently be applied for different materials. A rather sophisticated material model, incorporating gradient-enhanced damage coupled to plasticity in a geometrically non-linear setting, is used to demonstrate the capabilities of this approach. Two different strategies for the generation of training data are investigated and compared, and the neural network’s hyperparameters are optimised for improved prediction capabilities. In view of the calibration of material parameters related to the non-locality of the model, the obtained set of parameters is again considered as a starting value for a final optimisation step, where we consider inhomogeneous states of deformation and digital image correlation data.

Parameters Identification of Rubber-like Hyperelastic Material Based on General Regression Neural Network.

In this study, we present a systematic scheme to identify the material parameters in constitutive model of hyperelastic materials such as rubber. This approach is proposed based on the combined use of general regression neural network, experimental data and finite element analysis. In detail, the finite element analysis is carried out to provide the learning samples of GRNN model, while the results observed from the uniaxial tensile test is set as the target value of GRNN model. A problem involving parameters identification of silicone rubber material is described for validation. The results show that the proposed GRNN-based approach has the characteristics of high universality and good precision, and can be extended to parameters identification of complex rubber-like hyperelastic material constitutive.

Identification of friction coefficients and strain-compensated Arrhenius-type constitutive model by a two-stage inverse analysis technique

In this work, a two-stage inverse analysis technique is proposed to identify the friction coefficients during hot compression test of aluminum alloy 6N01 (AA6N01) and its material parameters in the strain-compensated Arrhenius-type constitutive model. Firstly, the minimal shape error between the measured and simulated specimen is set as the optimization objective. Based on the material parameters obtained by a traditional linear fitting method, the friction coefficient under each forming condition is obtained by the first-stage inverse analysis method. Secondly, on the basis of the obtained friction coefficients and taking the minimal error between the experimental and predicted forces as the optimization objective, 16 unified material parameters in the constitutive model are identified by the second-stage inverse analysis method. Then above two stages are combined together to realize loop calculation: the first-stage inverse analysis provides friction coefficients for the identification of material parameters while the second-stage updates new material parameters for identifying better friction coefficients. When the average error (Er (friction)) between friction coefficients obtained at the current and last loop is less than 5%, the whole identification process comes to the end and the optimized friction coefficients and material parameters are obtained. Results show that the maximum shape error is only 2.48%, which indicates that the obtained friction coefficients can reflect the practical lubrication conditions between the tooling head and specimens. Additionally, at low strain rates (0.01, 0.1 and 1s−1), the predicted forces have a good agreement with experimental ones. While at high strain rate (10s−1), some discrepancy exists between the predicted and experimental results and the maximum error arrives at 8.58%. But the global predicted error is only 4.2%, which verifies that the proposed model and obtained material parameters can describe well the rheological behavior of AA6N01 at elevated temperatures. By comparing the predicted forces obtained by the inverse analysis and traditional linear fitting method, it is found that the predicted forces by the inverse analysis are more close to experimental data. Therefore, it can be concluded that more accurate material parameters can be obtained and provided for the numerical simulation of the extrusion process of AA6N01 using the two-stage inverse analysis technique proposed in this paper.

Material parameter optimisation of Ohno-Wang kinematic hardening model using multi objective genetic algorithm

Ohno-Wang hardening model is an advanced constitutive model to evaluate the cyclic plasticity behaviour of material. This model has capability to simulate uniaxial and biaxial ratcheting response of the material. But, it is required to determine large number of material parameters from several experimental responses in order to simulate this phenomenon. Material parameters for constitutive models are generally determined manually through trial and error approach which is tedious and less accurate. Due to arbitrariness and complexity of cyclic loading, advanced constitutive material models become non-linear and multimodal in functional and parameter space. To overcome this problem, an automated parameter optimisation approach using genetic algorithm has been proposed in the present work to identify Ohno-Wang material parameters of 304LN, stainless steel for uniaxial simulation. Optimisation by this approach has improved the model prediction in uniaxial low cycle and ratcheting fatigue simulations after comparison with the experimental response.

Viscoelastic Characterization of Fiber-Reinforced Elastomeric Composites at Finite Strain

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.

Identification of material parameters in extended contiuum mechanicalmodels

AbstractA method for the identification of material parameters of constitutive models describing foamed materials is discussed in the present work. One can model foamed materials in two ways: using a lattice‐like micro‐model or alternatively a continuum mechanical approach. A beam model is used for the description of foams on a microscopic scale and alternatively an extended continuum model based on the Cosserat theory is employed on the macroscopic scale. By performing numerical shear tests at specimens of different sizes, we can observe the following effect on both models: The distribution of the rotations shows a strong boundary layer character at the top and bottom boundary of the specimen, whereas at the inner part it takes a constant value. These boundary layer effects do not scale with the size of the specimen, as a result specimens occur to be stiffer, see [1]. The goal is to perform a fitting of the Cosserat parameters by comparing the results of the macroscopic model to these of the microscopic one. The parameter fitting concerns an inverse problem which is treated within the framework of stochastic optimization methods. An evolutionary algorithm is used in combination with a response surface method for the identification of the material parameters. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Parameter Identification for Inelastic Constitutive Models

AbstractThe identification of material parameters of constitutive models is based on identification experiments. Since even specimens from the same lot show high deviations in the experimental data, the identification of the material parameters leads to different results for one and the same material. The number of identification experiments is usually not large enough for a statistical analysis of the deviations in the identified parameters. In order to overcome this problem we present a method of stochastic simulation which is based on time series analysis for generating artificial data with the same stochastic behaviour as the experimental data. The stochastic simulations allow an investigation of the confidence in the fits of the material parameters. We validate the stochastic simulations by comparing the results of the parameter identification from experimental data with the results from artificial data. The presented simulation method applied here turns out to be a suitable tool for generating artificial data for various kinds of analysis purposes. However, it is very important to take into account that the machines which perform the experiments do not maintain constant strain rates in the loading history of the tension and cyclic experiments.

Identification of material parameters in constitutive model for sheet metals from cyclic bending tests

This paper deals with the identification of material parameters in a constitutive model for sheet metals using the bending moment versus curvature diagrams obtained by cyclic bending tests. The model can describe the cyclic strain hardening by the isotropic hardening and the Bauschinger effect by the kinematic hardening. An optimization technique based on the iterative multipoint approximation concept was used for the identification of the material parameters. This paper describes the experimentation, the fundamentals and the technique of the identification problem, and the verification of this approach.

Identification of Material Parameters in Constitutive Models of Cyclic Plasticity from Bending Tests of Sheet Metals.

This paper deals with the identification of material parameters in constitutive models of cyclic plasticity for sheet metals using the bending moment vs. curvature diagrams obtained by cyclic bending tests. After a brief discussion on the identification for some simple plasticity models, a new identification method based on the iterative multipoint approximation concept is presented for complicated elastic-plastic consititutive models incorporating many numbers of material parameters. As an example, eight material parameters in Chaboche-Rosselier's model were identified by this method. This approach has been verified by comparing the simulated stress-strain curve using the constitutive model incorporating the identified material parameters with the experimental curve determined by uniaxial tension.