Sample shapes for reliable parameter identification in elasto-plasticity

Shutov, A. V.; Kaygorodtseva, A. A.

doi:10.1007/s00707-020-02758-9

Cited by 7 publications

(6 citation statements)

References 30 publications

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“…where dev( ) = ( ) − 𝐈tr( )∕3; according to elastic rule (3), deviatoric stress is expressed as dev(𝝈) = −2(𝜓 1 + 𝜓 2 𝐼 𝑐 1 )dev(𝐜 𝑒 ) + 2𝜓 2 dev(𝐜 𝑒 ) 2 .…”

Section: Solution For a Creep Law Based On Von Mises Equivalent Stressmentioning

confidence: 99%

“…The torsion of circular rods is easier to carry out, however, in this case, the stress is inhomogeneous and solutions of the corresponding boundary value problems are needed. Besides that, a combination of torsion tests for samples with homogeneous and heterogeneous deformation (for example, a solid cylinder and a thin-walled tube) gives more stable results for identifying material parameters than either one alone [2], so rod torsion can also be utilized in synthetic tests.…”

Section: Introductionmentioning

confidence: 99%

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Creep relaxation in nonlinear viscoelastic twisted rods

Sevastyanov

2022

Z Angew Math Mech

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The solution to the problem of stress relaxation in a twisted nonlinear viscoelastic isotropic incompressible rod is presented. We address the multiplicative decomposition of the deformation gradient into reversible (elastic) and irreversible (creep) parts. The elastic potential and the creep potential can be chosen arbitrarily. In particular, the creep law can take into account both the nonlinearity of the relationship between the strain rate and the effective stress, and timehardening or softening. We consider two variants of creep constitutive relations. One is based on the Tresca equivalent stress, the other is based on the von Mises equivalent stress. The first of them leads to a significant simplification of the governing equations because in this case a radial elastic strain vanishes. In this framework, we obtain a closed-form solution in elementary functions for the coupling of Mooney-Rivlin elastic model and linear creep law. For the von Mises material, numerical-analytical results are obtained. The results are compared with the known small-strain solutions.

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Section: Solution For a Creep Law Based On Von Mises Equivalent Stressmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Creep relaxation in nonlinear viscoelastic twisted rods

Sevastyanov

2022

Z Angew Math Mech

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“…For reproducibility of results and faster convergence of Monte Carlo computations, the quasi-Monte Carlo method is implemented in the current study (cf. [24,32]). The quasi-Monte Carlo method differs from the classical in using a low-discrepancy sequence of random numbers.…”

Section: Basic Steps Of Sensitivity Analysismentioning

confidence: 99%

“…Appendix A: Fast computation of p (j) We discuss a quick computation of the parameter vectors p (j) ∈ R n , corresponding to jth draws of noisy data. The procedure is the same as in [32]. Recall that − − → Exp ∈ R Nexp is the vector of available experimental data, −−→ M od( p) ∈ R Nexp is the corresponding modelling response, p = ( p c , p K ) ∈ R n is the vector of unknown material parameters.…”

Section: Appendix B: Correlation Matricesmentioning

confidence: 99%

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Inspection of ratcheting models for pathological error sensitivity and overparametrization

Kaygorodtseva¹,

Shutov²

2021

Preprint

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Accurate analysis of plastic strain accumulation under stress-controlled cyclic loading is vital for numerous engineering applications. Typically, models of plastic ratcheting are calibrated against available experimental data. Since actual experiments are not exactly accurate, one should check the identification protocols for pathological dependencies on experimental errors. In this paper, a step-by-step algorithm is presented to estimate the sensitivities of identified material parameters. As a part of the sensitivity analysis method, a new mechanics-based metric in the space of material parameters is proposed especially for ratchetingrelated applications. The sensitivity of material parameters to experimental errors is estimated, based on this metric. For demonstration purposes, the accumulation of irreversible strain in the titanium alloy VT6 (Russian analog of Ti-6Al-4V) is analysed. Three types of phenomenological models of plastic ratcheting are considered. They are the Armstrong-Frederick model as well as the first and the second Ohno-Wang models. Based on real data, a new rule of isotropic hardening is proposed for greater accuracy of simulation. The ability of the sensitivity analysis to determine reliable and unreliable parameters is demonstrated. The plausibility of the new method is checked by alternative approaches, like the consideration of correlation matrices and validation of identified parameters on "unseen" data. A relation between pathological error sensitivity and overparametrization is established.

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Uniaxial ratcheting and ductile damage in structural steel with a stochastic spreading of experimental data

Shutov,

Kaygorodtseva,

Zakharchenko

et al. 2024

Z Angew Math Mech

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This paper provides new experimental data regarding inelastic strain accumulation in structural steel samples. The samples are subjected to stress‐controlled cyclic loading with positive mean stress within each cycle; the loading blocks are combined in a complex pattern to study the effect of load history. A large‐strain ratcheting model is constructed based on a material law with a nonlinear kinematic and isotropic hardening. A new rule of ductile damage accumulation is suggested and a class of models with hardening stagnation is introduced. We show that models which include the hardening stagnation describe the experimental data more accurately. Unfortunately, due to a large spread of mechanical properties from sample to sample, it is impossible to describe the entire set of experiments using a single set of parameters. To address this challenge, we have developed novel mathematical tools for parameter identification in the context of stochastic variations in mechanical properties. These tools include the concept of a collar of model responses and the notion of protrusion. We propose an extended parameter identification problem that rethinks the standard error functional. We demonstrate that the extended identification problem effectively accounts for the large spread observed in experimental data when applied to the developed ratcheting model.

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Sample shapes for reliable parameter identification in elasto-plasticity

Cited by 7 publications

References 30 publications

Creep relaxation in nonlinear viscoelastic twisted rods

Creep relaxation in nonlinear viscoelastic twisted rods

Inspection of ratcheting models for pathological error sensitivity and overparametrization

Uniaxial ratcheting and ductile damage in structural steel with a stochastic spreading of experimental data

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