On the local identifiability of constituent stress–strain laws for hyperelastic composite materials

Sewerin, Fabian

doi:10.1007/s00466-019-01798-w

Cited by 5 publications

(4 citation statements)

References 40 publications

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“…However, this does not mean that the material parameters are addressed by the experiments. This issue is linked to the theory of the identifiability of material parameters [10] and discussed in connection with questions of solid mechanics by Hartmann and Gilbert [36,39], Hartmann et al [38], Sewerin [91], and Hartmann and Gilbert [37].…”

Section: General Remarks On Least-square Identificationmentioning

confidence: 99%

Parameter estimation and its influence on layered metal–composite–metal plates simulation

et al. 2022

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Laminates made of metal—glass fiber-reinforced polymers—metal layers require material parameters for each constitutive model of the constituents. First, although parameter identification for metallic materials has been frequently discussed, the stepwise identification of material parameters in terms of uncertainties of previously determined parameters is investigated by the concept of error propagation. Second, the calibration of a model of orthotropy describing the large deformation behavior of the glass fiber-reinforced kernel layer is a challenging process, especially against the background of a reliable determination of the parameters. The main problem is related to the lack of available experiments. This issue is embedded in the concept of local identifiability. Thus, the article provides experiments to determine the parameters of both the steel as well as the glass fiber-reinforced polymers. Particularly for the latter issue, $$\mu $$ μ -CT data is chosen to provide a representative volume element, where all deformation modes can be investigated. In this sense, a concept to determine all material parameters in a locally unique and reliable manner is studied. A linear error propagation concept provides the uncertainty of the resulting material parameters of the whole parameter set for the homogenized material. The entire parameter identification process is discussed thoroughly, and validation examples such as bending and deep drawing in metal forming processes, are provided to estimate the prediction accuracy. In this respect, the uncertainties found by parameter identification are applied to the prediction of finite element simulations of layered metal–composite–metal forming processes and error propagation is used to estimate the uncertainties of the simulations. In this contribution, we restrict ourselves to experiments at room temperature.

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Section: General Remarks On Least-square Identificationmentioning

confidence: 99%

Parameter estimation and its influence on layered metal–composite–metal plates simulation

et al. 2022

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“…In this context, the physical meaning of the parameters becomes questionable. This was mentioned in [4,7] for the general case in parameter identification, and studied in solid mechanics in [25,33,71]. Since this is only a local concept in the solution found by some optimizer, it is merely an indicator (so far, however, it appears to be quite a useful indicator).…”

Section: Quality Measuresmentioning

confidence: 99%

“…Moreover, most contributions do not discuss quality measures describing the resulting material parameters, such as the confidence interval, or the correlation between the parameters. Additionally, we follow the concept of local identifiability proposed in [4,7] which was studied in [25,71] in the field of solid mechanics.…”

Section: Introductionmentioning

confidence: 99%

Material parameter identification using finite elements with time-adaptive higher-order time integration and experimental full-field strain information

Hartmann

Gilbert

2021

Comput Mech

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In this article, we follow a thorough matrix presentation of material parameter identification using a least-square approach, where the model is given by non-linear finite elements, and the experimental data is provided by both force data as well as full-field strain measurement data based on digital image correlation. First, the rigorous concept of semi-discretization for the direct problem is chosen, where—in the first step—the spatial discretization yields a large system of differential-algebraic equation (DAE-system). This is solved using a time-adaptive, high-order, singly diagonally-implicit Runge–Kutta method. Second, to study the fully analytical versus fully numerical determination of the sensitivities, required in a gradient-based optimization scheme, the force determination using the Lagrange-multiplier method and the strain computation must be provided explicitly. The consideration of the strains is necessary to circumvent the influence of rigid body motions occurring in the experimental data. This is done by applying an external strain determination tool which is based on the nodal displacements of the finite element program. Third, we apply the concept of local identifiability on the entire parameter identification procedure and show its influence on the choice of the parameters of the rate-type constitutive model. As a test example, a finite strain viscoelasticity model and biaxial tensile tests applied to a rubber-like material are chosen.

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“…The presented identifiability index is based on the eigenvalues of the respective Hessian matrix of the optimization problem in the FEMU context. In the field of solid mechanics, exemplary studies regarding the local identifiability are conducted by [27] and [70]. However, thermal material parameters are only studied in the context of thermo‐mechanical material models, but not for the purely thermal case.…”

Section: Introductionmentioning

confidence: 99%

Identification of the thermal conductivity tensor for transversely isotropic materials

Tröger

Hartmann

2022

GAMM-Mitteilungen

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The knowledge of the thermal conductivities is of particular interest for the thermo‐mechanical modeling of transversely isotropic composite materials. Hence, the identification of these material parameters by solving an inverse problem is significant, as they cannot be directly measured. In this study, a suitable experimental setup is presented, where infrared thermography is used to measure the surface temperatures of thin specimens. Further, a local identifiability concept is employed to study whether locally unique parameters can be obtained. This leads to a particular step‐wise identification concept. The parameter identification is performed applying a nonlinear least‐square approach and finite elements. In the step‐wise identification process the convection coefficient is required first, and, subsequently, the coefficients of the thermal conductivity tensor are determined. Due to the step‐wise identification, the uncertainties of previously identified parameters have to be considered in the subsequent identification steps. The resulting uncertainties are estimated using the Gaussian error propagation concept. It turns out that the thermal conductivities of transversely isotropic materials are generally identifiable from surface temperature data. Furthermore, since all uncertainties have an essential influence on the results of real numerical simulations, their error propagation should be considered in resulting boundary‐value problems. Thus, the uncertainty quantification is demonstrated by a validation experiment.

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On the local identifiability of constituent stress–strain laws for hyperelastic composite materials

Cited by 5 publications

References 40 publications

Parameter estimation and its influence on layered metal–composite–metal plates simulation

Parameter estimation and its influence on layered metal–composite–metal plates simulation

Material parameter identification using finite elements with time-adaptive higher-order time integration and experimental full-field strain information

Identification of the thermal conductivity tensor for transversely isotropic materials

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