Identifiability of material parameters in solid mechanics

Hartmann, Stefan; Gilbert, Rose Rogin

doi:10.1007/s00419-017-1259-4

Cited by 41 publications

(36 citation statements)

References 59 publications

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“…is can be interpreted as both adverse and favourable effects. e negative aspect is the considerable sensitivity to finding different local minima in the error hypersurface and lack of the absolute minimum finding algorithm, but the positive is that, first, this can be to some extent countermanded and that, second, weights do not refer to physical material properties (compare [43]), in the mechanical sense, but are constants in mathematical expressions enabling the network to find local minima. e first step to at least partially diminish the disadvantageous randomness influence is to understand the phenomenon and input data possibly well (we are referring here to the general approximation theorem [44]).…”

Section: Approximation Within and Extrapolation Outside The Density Imentioning

confidence: 99%

ANN Architecture Specifications for Modelling of Open-Cell Aluminum under Compression

Dudzik

Stręk

2020

Mathematical Problems in Engineering

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e knowledge on strength properties of porous metals in compression is essential in tailored application design, as well as in elaboration of general material models. In this article, the authors propose specification details of the ANN architecture for adequate modelling of the phenomenon of compressive behaviour of open-cell aluminum. In the presented research, an algorithm was used to build different structures of artificial neural networks (ANNs), which approximated stress-strain relations of an aluminum sponge subjected to compression. Next, the quality of the built approximations was appraised. e mean absolute relative error (MARE), coefficient of determination between outputs and targets (R 2 ), root mean square error (RMSE), and mean square error (MSE) were assumed as criterial measures for the assessment of the fitting quality. e studied neural networks (NNs) were two-layer feedforward networks with different numbers of neurons in the hidden layer. A set of experimental stress-strain data from quasistatic uniaxial compression tests of open-cell aluminum of various apparent densities was used as data for training of neural networks. Analysis was performed in two modes: in the first one, all samples were taken for training, and in the second case, one sample was left out during training in order to play the role of external data for testing the trained network later. e taken out samples were maximum and minimum density samples (for extrapolation) and one random from within the density interval. e results showed that good approximation on the engineering level (MARE < 5%) was reached for teaching networks with ≥7 neurons in the hidden layer for the first studied case and with ≥8 neurons for the second. Calculations on external data proved that 8 neurons are enough to actually obtain MARE < 10%. Moreover, it was shown that the quality of approximation can be significantly improved to MARE ≈ 7% (tested on external data) if the initial region of the stress-strain relation is modelled by an additional network.

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Section: Approximation Within and Extrapolation Outside The Density Imentioning

confidence: 99%

ANN Architecture Specifications for Modelling of Open-Cell Aluminum under Compression

Dudzik

Stręk

2020

Mathematical Problems in Engineering

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“…Further schemes are connected to dynamical tests to identify elastic material parameters . To address more material parameters—particularly, from constitutive models with internal variables—several tests have to be incorporated, see discussion in Hartmann and Gilbert. In Refs.…”

Section: Parameter Identificationmentioning

confidence: 99%

“…The closer D r is to zero, the more sensitive the optimization result is to small perturbations. This concept is studied for solid mechanical problems in detail in Hartmann and Gilbert …”

Section: Parameter Identificationmentioning

confidence: 99%

Basic studies in biaxial tensile tests

2018

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Biaxial tensile experiments are an increasing test alternative of thin‐walled specimens to characterize the material behavior under mechanical agencies. This is mainly driven by digital image correlation systems to obtain information about the surface deformation. However, it is not as simple as a tensile test since we can only measure the deformation in a region on the specimen and not the stress state. The latter aspect of stress determination is discussed as well. In this article, we address several basic questions. First: can we obtain a homogenous strain state in cruciform‐like specimens? In this sense the shape will be discussed and a measure of homogeneity is introduced for proofing whether homogeneity can be guaranteed. Second: how can we reach large strains in the center of the specimens? This is connected to the specimen's geometry (arm reinforcement, slots, thinning of center, …). Furthermore, we discuss the problem of material parameter identification using biaxial tensile test information, which is connected to the concept of identifiability using finite elements. This is discussed at the simplest constitutive model, namely linear isotropic elasticity. Thus, the overall goal is connected to a critical review on biaxial experiments using cruciform specimens. The test materials are polymers.

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“…Thus, re-identification of "synthetic experimental data" (i.e. numerically generated, unperturbed data by the model) is a method of choice to find out whether identifiability is given, see [18,19]. Even for very simple models and tests, for example, equibiaxial tensile test for linear, isotropic elasticity, it turns out that identifiability of the parameters in principal is not given, [19].…”

Section: Introductionmentioning

confidence: 99%

From Experiment to Material Parameter Identification

Hartmann

Gilbert

2018

Proc Appl Math and Mech

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Constitutive modeling requires the calibration of the constitutive model to experimental data. This calibration is called material parameter identification. Simple experiments lead to specified deformation and stress states, which is not guaranteed in all situation. Thus, finite elements must be drawn on to calculate the deformation state solving the entire boundary-value problem. There are several basic questions, which must be addressed apart from experiments doable for the material under consideration: first, what optimization technique is suitable? Second, are the material parameters identifiable by the given experiments, and what is the quality of the result? Third, there have been open questions of the connection between engineering and mathematical literature showing that in Engineering Science the procedures have already been developed in Numerical Mathematics. These question will be discussed in this overview.

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Identifiability of material parameters in solid mechanics

Cited by 41 publications

References 59 publications

ANN Architecture Specifications for Modelling of Open-Cell Aluminum under Compression

ANN Architecture Specifications for Modelling of Open-Cell Aluminum under Compression

Basic studies in biaxial tensile tests

From Experiment to Material Parameter Identification

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