pith. sign in

arxiv: 1906.10647 · v1 · pith:4DB5CAYYnew · submitted 2019-06-21 · 💻 cs.CE

Parameter Identification in Viscoplasticity using Transitional Markov Chain Monte Carlo Method

Ehsan Adeli , Hermann G. Matthies This is my paper

Pith reviewed 2026-05-25 18:28 UTC · model grok-4.3

classification 💻 cs.CE
keywords parameter identificationviscoplasticityBayesian inferenceTMCMCChaboche modelhardening parameterssurface displacementartificial data
0
0 comments X

The pith

TMCMC in a Bayesian setting recovers Chaboche viscoplastic parameters from surface displacement vectors alone.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that Transitional Markov Chain Monte Carlo sampling can estimate the parameters of a Chaboche viscoplastic model when the only available observations are surface displacement measurements. Artificial data are first generated to incorporate realistic measurement noise and specimen variability, then the method is applied under uniform priors that encode no prior knowledge. The study checks how many such measurements are required to recover the true hardening and model parameters to acceptable accuracy. A reader would care because the approach directly addresses the difficulty of identifying parameters in highly nonlinear constitutive models when only limited, noisy data are available.

Core claim

The central claim is that it is possible to identify the model and hardening parameters of a viscoplastic model with only a surface displacement measurement vector in the Bayesian setting using TMCMC and to evaluate the number of measurements needed for a very acceptable estimation of the uncertain parameters of the model.

What carries the argument

Transitional Markov Chain Monte Carlo (TMCMC) method for drawing samples from the posterior distribution of the model parameters given the displacement data.

If this is right

  • The identified parameters match the true values used to generate the artificial data.
  • Surface displacement vectors alone are sufficient for identification of the high-nonlinearity Chaboche model.
  • The number of required measurements can be determined for acceptable estimation accuracy.
  • Uniform priors suffice to obtain useful posterior estimates when no prior information is available.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same workflow could be tested on other viscoplastic or plastic constitutive models that lack closed-form solutions for parameter recovery.
  • If the artificial-data assumption holds only approximately, real experiments would still need a separate validation step against independent test data.
  • Reducing the required number of measurements could lower the cost of material characterization campaigns that currently rely on multiple full-field strain measurements.

Load-bearing premise

The artificial data generated by the stochastic simulation technique exhibit the same stochastic behavior as real experimental data, including measurement errors and specimen-to-specimen differences.

What would settle it

Apply the same TMCMC procedure to real experimental displacement data from cyclic tests on steel specimens and check whether the recovered parameters reproduce the measured responses within the posterior uncertainty bands.

Figures

Figures reproduced from arXiv: 1906.10647 by Ehsan Adeli, Hermann G. Matthies.

Figure 1
Figure 1. Figure 1: Boundary condition considered The normal tractions, which is a Neumann boundary condition, are ap￾plied cyclically [55, 56, 57] in x, y and z directions on front and back faces and the magnitude of tractions in all directions are shown in [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Decomposed applied force at point E according to time [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Displacement of point E in x, y and z directions according to time The displacements of point E in x, y and z directions are noted as the virtual data in this case. The Transitional Markov chain Monte Carlo method is applied using sampling by which 1000 samples are generated and the history of the dis￾placement of point E is noted. The determined prior and posterior proba￾bility density functions are compa… view at source ↗
Figure 4
Figure 4. Figure 4: Prior distribution of the parameters 1.4 1.6 1.8 x 108 σ y 40 50 60 b χ 40 60 80 bR 7.6 7.7 7.8 x 108 G 1.6 1.7 1.8 x 109 1.4 1.6 1.8 x 108 κ σ y 40 50 60 b χ 40 60 80 b R 7.6 7.7 7.8 x 108 G 1.6 1.7 1.8 x 109 κ [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Posterior distribution of the parameters [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
read the original abstract

To evaluate the cyclic behavior under different loading conditions using the kinematic and isotropic hardening theory of steel, a Chaboche viscoplastic material model is employed. The parameters of a constitutive model are usually identified by minimization of the difference between model response and experimental data. However, measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article, the Choboche model is used and a stochastic simulation technique is applied to generate artificial data which exhibit the same stochastic behavior as experimental data. Then the model parameters are identified by applying an estimation using Bayes's theorem. The Transitional Markov Chain Monte Carlo method (TMCMC) is introduced and employed to estimate the model parameters in the Bayesian setting. The uniform distributions of the parameters representing their priors are considered which literally means no knowledge of the parameters is available. Identified parameters are compared with the true parameters in the simulation, and the efficiency of the identification method is discussed. In fact, the main purpose of this study is to observe the possibility of identifying the model and hardening parameters of a viscoplastic model as a very high non-linear model with only a surface displacement measurement vector in the Bayesian setting using TMCMC and evaluate the number of measurements needed for a very acceptable estimation of the uncertain parameters of the model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript describes a Bayesian parameter identification workflow for the Chaboche viscoplastic model (with kinematic and isotropic hardening) under cyclic loading. Synthetic displacement data are generated by a stochastic simulation technique asserted to reproduce experimental measurement noise and specimen variability; TMCMC sampling with uniform priors is then used to recover the model parameters from surface displacement vectors alone. The central claims are that acceptable posterior estimates are obtained and that the minimum number of measurements required for such estimates can be quantified by comparing recovered values to the known simulation inputs.

Significance. If the synthetic data generation step is shown to reproduce the statistical properties of real displacement measurements, the approach would supply a practical route to uncertainty-aware identification of a highly nonlinear constitutive model from limited surface data, which is relevant to computational solid mechanics applications where full-field or multi-axial experiments are expensive.

major comments (2)
  1. [Abstract] Abstract: the claim that 'a stochastic simulation technique is applied to generate artificial data which exhibit the same stochastic behavior as experimental data' is load-bearing for all subsequent posterior results and measurement-count conclusions, yet the manuscript supplies no quantitative validation (e.g., comparison of empirical covariance, power spectra, or specimen-to-specimen variance) that the chosen noise model and correlation structure match physical cyclic-test statistics.
  2. [Abstract / Methods (data generation)] The weakest assumption identified in the reader's report is exactly the point above; without that demonstration the reported credible intervals and 'very acceptable estimation' statements remain conditional on an unverified generative model and do not yet support the claim for real experimental data.
minor comments (1)
  1. [Abstract] Abstract contains the spelling 'Choboche' (should be Chaboche).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address the major comments point by point below, proposing revisions to qualify claims about the synthetic data where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'a stochastic simulation technique is applied to generate artificial data which exhibit the same stochastic behavior as experimental data' is load-bearing for all subsequent posterior results and measurement-count conclusions, yet the manuscript supplies no quantitative validation (e.g., comparison of empirical covariance, power spectra, or specimen-to-specimen variance) that the chosen noise model and correlation structure match physical cyclic-test statistics.

    Authors: We agree that the manuscript does not supply quantitative validation (such as covariance or spectral comparisons) of the synthetic data against real experimental statistics. The stochastic simulation adds noise to displacement fields from the true parameters to represent measurement errors and variability, but the study evaluates TMCMC recovery against known true values rather than matching a specific experimental dataset. We will revise the abstract and methods to state that the artificial data are generated with noise characteristics intended to be representative of typical experimental conditions, without claiming an exact statistical match. This will make the reported posteriors and measurement-count conclusions explicitly conditional on the assumed generative model. revision: yes

  2. Referee: [Abstract / Methods (data generation)] The weakest assumption identified in the reader's report is exactly the point above; without that demonstration the reported credible intervals and 'very acceptable estimation' statements remain conditional on an unverified generative model and do not yet support the claim for real experimental data.

    Authors: We concur that the credible intervals and statements of acceptable estimation are conditional on the generative model for the synthetic data. The manuscript's core contribution is demonstrating TMCMC-based recovery of known true parameters from surface displacement vectors in this controlled setting; it does not present or claim results from real experimental data. We will revise the abstract, introduction, and discussion to emphasize this conditional nature and to note that extension to physical experiments would require separate validation of the noise model. No alterations to the TMCMC implementation or numerical results are needed. revision: yes

Circularity Check

0 steps flagged

No circularity: standard synthetic-data recovery of known parameters via TMCMC

full rationale

The paper generates synthetic displacement data from the Chaboche model using known true parameters plus an explicit noise model, then applies standard Bayesian updating with uniform priors and TMCMC to recover posterior estimates of those same parameters. Recovered values are compared directly to the known simulation inputs. This is a conventional validation exercise on synthetic benchmarks; no equation reduces a claimed prediction to a fitted input by construction, no uniqueness theorem is imported via self-citation, and no ansatz is smuggled. The chain is self-contained against the internal synthetic benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard Bayesian inference and the assumption that the chosen constitutive model plus artificial data generation faithfully represent the identification task; no additional free parameters or invented entities are introduced beyond the model parameters being estimated.

axioms (2)
  • standard math Bayes theorem can be used to update parameter distributions from displacement data
    Invoked as the basis for the TMCMC estimation procedure.
  • domain assumption The Chaboche viscoplastic model with kinematic and isotropic hardening correctly describes the cyclic behavior of steel
    Required for the identified parameters to be meaningful for the intended application.

pith-pipeline@v0.9.0 · 5753 in / 1248 out tokens · 28379 ms · 2026-05-25T18:28:11.354218+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages · 2 internal anchors

  1. [1]

    A. Miller. An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part I–Equations Development and Analytical Procedures. J. Eng. Mater. Technol. 98(2), 97-105, 1976

    work page 1976

  2. [2]

    Krempl, J

    E. Krempl, J. J. McMahon, and D. Yao. Viscoplasticity Based on Over- stress with a Differential Growth Law for the Equilibrium Stress. Me- chanics of Materials 5, 35-48, 1986

    work page 1986

  3. [3]

    R. K. Korhonen, M. S. Laasanen, J. Toyras, R. Lappalainen, H. J. Helminen, and J. S. Jurvelin. Fibril reinforced poroelastic model pre- dicts specifically mechanical behavior of normal, proteoglycan de- pleted and collagen degraded articular cartilage. J Biomech 36, 1373- 1379

    work page

  4. [4]

    Gill, and Branko Ladanyi

    Michel Aubertin, Denis E. Gill, and Branko Ladanyi. A unified vis- coplastic model for the inelastic flow of alkali halides. Mechanics of Materials 11, 63-8, 1991

    work page 1991

  5. [5]

    K. S. Chan, S. R. Bodner, A.F. Fossum, and D.E. Munson. A consti- tutive model for inelastic flow and damage evolution in solids under triaxial compression. Mechanics of Materials 14, 1-14, 1992

    work page 1992

  6. [6]

    J. L. Chaboche, and G. Rousselier. On the plastic and viscoplastic con- stitutive equations - part 1: rules developed with internal variable con- cept. J. Press. Vessel Technol., 105, 153-158, 1983

    work page 1983

  7. [7]

    J. L. Chaboche, and G. Rousselier. On the plastic and viscoplastic con- stitutive equations - part 2: application of internal variable concepts to the 316 stainless steel. J. Press. Vessel Technol., 105, 159-164, 1983

    work page 1983

  8. [8]

    Kłosowski, and A

    P. Kłosowski, and A. Mleczek. Parameters’ Identification of Perzyna and Chaboche Viscoplastic Models for Aluminum Alloy at Tempera- ture of 120◦C. Engng. Trans. 62, 3, 291-305, 2014

    work page 2014

  9. [9]

    Y . Gong, C. Hyde, W. Sun, and T. Hyde. Determination of material properties in the Chaboche unified viscoplasticity model. Journal of Materials Design and Applications, 224(1), 19-29, 2010. 14

    work page 2010

  10. [10]

    Harth, and J ¨urgen Lehn

    T. Harth, and J ¨urgen Lehn. Identification of Material Parameters for In- elastic Constitutive Models Using Stochastic Methods. GAMM-Mitt. 30, No. 2, 409-429, 2007

    work page 2007

  11. [11]

    K. S. Chan, S. R. Bodner, and U. S. Lindholm. Phenomenological Modelling of Hardening and Thermal Recovery in Metals. Journal of Engineering Materials and Technology 110, 1-8, 1988

    work page 1988

  12. [12]

    Pacheco, G

    C. Pacheco, G. S. Dulikravich, M. Vesenjak, M. Borovinsek, I. M. A. Duarte, R. Jha, S. R. Reddy, H. R. B. Orlande and M. J. Colaco. Inverse parameter identification in solid mechanics using Bayesian statistics, response surfaces and minimization. Technische Mechanik 36(1-2), 120-131, 2016

    work page 2016

  13. [13]

    Gallina, L

    A. Gallina, L. Ambrozinski, P. Packo, L. Pieczonka, T. Uhl and W. J. Staszewski. Bayesian parameter identification of orthotropic compos- ite materials using lamb waves dispersion curves measurement. Journal of Vibration and Control 23(16), 2656-2671, 2017

    work page 2017

  14. [14]

    Pieczonka, A

    L. Pieczonka, A. Gallina, L. Ambrozinski, P. Packo, T. Uhl and W. J. Staszewski. Parameters identification of composite materials using Bayesian approach and guided ultrasonic waves. Proceedings of ISMA 2016 - International Conference on Noise and Vibration Engineering and USD2016, 2016

    work page 2016

  15. [15]

    Arnst, R

    M. Arnst, R. Ghanem and C. Soize. Identification of Bayesian poste- riors for coefficients of chaos expansions. Journal of Computational Physics 229(9), 3134-3154, 2010

    work page 2010

  16. [16]

    Bayesian inference for the stochastic identification of elastoplastic material parameters: Introduction, misconceptions and insights

    H. Rappel, L. A. A. Beex, J. S. Hale and S. P. A. Bordas. Bayesian in- ference for the stochastic identification of elastoplastic material param- eters: introduction, misconceptions and insights. arXiv:1606.02422, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  17. [17]

    Rappel, L

    H. Rappel, L. A. A. Beex, L. Noels and S. P. A. Bordas. Identifying elastoplastic parameters with Bayes’ theorem considering double error sources and model uncertainty. Journal of Probabilistic Engineering Mechanics, 2018

    work page 2018

  18. [18]

    M. Słonski. Bayesian identification of elastic parameters in composite laminates applying lamb waves monitoring. Computational Methods in Structural Dynamics and Earthquake Engineering, M. Papadrakakis, V . Papadopoulos, V . Plevris (Eds.), 2015

    work page 2015

  19. [19]

    D. An, J. Cho and N. H. Kim. Identification of correlated damage parameters under noise and bias using Bayesian inference. Structural Health Monitoring 11(3), 293-303, 2011

    work page 2011

  20. [20]

    W. P. Hernandez, F. C. L. Borges, D. A. Castello, N. Roitman and C. Magluta. Bayesian inference applied on model calibration of a frac- 15 tional derivative viscoelastic model. Proceedings of the XVII Interna- tional Symposium on Dynamic Problems of Mechanics, V . Steffen, D. A. Rade, W. M. Bessa (Eds.), 2015

    work page 2015

  21. [21]

    R. Mahnken. Identification of material parameters for constitutive equations. Encyclopedia of Computational Mechanics Second Edition, Part 2. Solids and Structures, 1-21, 2017

    work page 2017

  22. [22]

    Zheng and Y

    W. Zheng and Y . Yu. Bayesian probabilistic framework for damage identification of steel truss bridges under joint uncertainties. Advances in Civil Engineering 1-13, 2013

    work page 2013

  23. [23]

    J. M. Nichols, E. Z. Moore and K. D. Murphy. Bayesian identifica- tion of a cracked plate using a population-based Markov Chain Monte Carlo method. Journal of Computers and Structures 89(13-14), 1323- 1332, 2011

    work page 2011

  24. [24]

    Zhang, J

    E. Zhang, J. D. Chazot and J. Antoni. Parametric identification of elas- tic modulus of polymeric material in laminated glasses. 16th IFAC Symposium on System Identification, The International Federation of Automatic Control, 2012

    work page 2012

  25. [25]

    Madireddy, B

    S. Madireddy, B. Sista and K. Vemaganti. A Bayesian approach to se- lecting hyperelastic constitutive models of soft tissue. Journal of Com- putational and Applied Mathematics 291, 102-122, 2015

    work page 2015

  26. [26]

    Wang and N

    J. Wang and N. Zabaras. A Bayesian inference approach to the in- verse heat conduction problem. International Journal of Heat and Mass Transfer 47(17-18), 3927-3941, 2004

    work page 2004

  27. [27]

    C. K. Oh, J. L. Beck and M. Yamada. Bayesian learning using auto- matic relevance determination prior with an application to earthquake early warning. Journal of Engineering Mechanics 134(12), 1013-1020, 2008

    work page 2008

  28. [28]

    K. Alvin. Finite element model update via Bayesian estimation and minimization of dynamic residuals. The American Institute of Aero- nautics and Astronautics Journal 135(5), 879-886, 1997

    work page 1997

  29. [29]

    Marwala and S

    T. Marwala and S. Sibusiso. Finite element model updating using Bayesian framework and modal properties. Journal of Aircraft 42(1), 275-278, 2005

    work page 2005

  30. [30]

    Daghia, S

    F. Daghia, S. de Miranda, F. Ubertini and E. Viola. Estimation of elas- tic constants of thick laminated plates within a Bayesian framework. Journal of Composite Structures 80(3), 461-473, 2007

    work page 2007

  31. [31]

    Abhinav and C

    S. Abhinav and C. Manohar. Bayesian parameter identification in dy- namic state space models using modified measurement equations. In- ternational Journal of Non-Linear Mechanics 71, 89-103, 2015. 16

    work page 2015

  32. [32]

    C. Gogu, W. Yin, R. Haftka, P. Ifju, J. Molimard, R. le Riche and A. Vautrin. Bayesian identification of elastic constants in multi- directional laminate from Moire interferometry displacement fields. Journal of Experimental Mechanics 53(4), 635-648, 2013

    work page 2013

  33. [33]

    C. Gogu, R. Haftka, J. Molimard and A. Vautrin. Introduction to the Bayesian approach applied to elastic constants identification. The American Institute of Aeronautics and Astronautics Journal 48(5), 893-903, 2010

    work page 2010

  34. [34]

    P. S. Koutsourelakis. A novel Bayesian strategy for the identification of spatially varying material properties and model validation: an applica- tion to static elastography. International Journal for Numerical Meth- ods in Engineering 91(3), 249-268, 2012

    work page 2012

  35. [35]

    P. S. Koutsourelakis. A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters. Journal of Computational Physics 228(17), 6184-6211, 2009

    work page 2009

  36. [36]

    D. D. Fitzenz, A. Jalobeanu and S. H. Hickman. Integrating laboratory creep compaction data with numerical fault models: a Bayesian frame- work. Journal of Geophysical Research: Solid Earth 112, B08410, 2007

    work page 2007

  37. [37]

    T. Most. Identification of the parameters of complex constitutive mod- els: least squares minimization vs. Bayesian updating. In: Straub, D. (ed.) Reliability and Optimization of Structural Systems, CRC Press, 119-130, 2010

    work page 2010

  38. [38]

    Sarkar, D

    S. Sarkar, D. S. Kosson, S. Mahadevan, J. C. L. Meeussen, H. van der Sloot, J. R. Arnold, K. G. Brown. Bayesian calibration of thermo- dynamic parameters for geochemical speciation modeling of cementi- tious materials. Journal of Cement and Concrete Research 42(7), 889- 902, 2012

    work page 2012

  39. [39]

    Zhang, J

    E. Zhang, J. D. Chazot, J. Antoni and M. Hamdi. Bayesian charac- terization of Young’s modulus of viscoelastic materials in laminated structures. Journal of Sound and Vibration 332(16), 3654-3666, 2013

    work page 2013

  40. [40]

    Mehrez, E

    L. Mehrez, E. Kassem, E. Masad and D. Little. Stochastic identifica- tion of linear-viscoelastic models of aged and unaged asphalt mixtures. Journal of Materials in Civil Engineering 27(4), 04014149, 2015

    work page 2015

  41. [41]

    Miles, M

    P. Miles, M. Hays, R. Smith and W. Oates. Bayesian uncertainty anal- ysis of finite deformation viscoelasticity. Journal of Mechanics of Ma- terials 91, 35-49, 2015

    work page 2015

  42. [42]

    Zhao and A

    X. Zhao and A. A. Pelegri. A Bayesian approach for characterization of soft tissue viscoelasticity in acoustic radiation force imaging. In- ternational Journal for Numerical Methods in Biomedical Engineering 32(4), E02741, 2016. 17

    work page 2016

  43. [43]

    Z. R. Kenz, H. T. Banks and R. C. Smith. Comparison of frequentist and Bayesian confidence analysis methods on a viscoelastic stenosis model. SIAM/ASA Journal on Uncertainty Quantification 1(1), 348- 369, 2013

    work page 2013

  44. [44]

    D. An, J. Choi, N. H. Kim and S. Pattabhiraman. Fatigue life prediction based on Bayesian approach to incorporate field data into probability model. Journal of Structural Engineering and Mechanics 37(4), 427- 442, 2011

    work page 2011

  45. [45]

    J. Velde. 3D Nonlocal Damage Modeling for Steel Structures under Earthquake Loading. Department of Architecture, Civil Engineering and Environmental Sciences University of Braunschweig - Institute of Technology, 2010

    work page 2010

  46. [46]

    Q. S. Nguyen. Mechanical Modeling of Anelasticity. Revue de Physique Appliquee 23(4), 325-330, 1988

    work page 1988

  47. [47]

    J. L. Beck and S. K. Au. Bayesian updating of structural models and reliability using Markov Chain Monte Carlo simulation. Journal of En- gineering Mechanics 128(4), 380-391, 2002

    work page 2002

  48. [48]

    Ching and Y

    J. Ching and Y . C. Chen. Transitional Markov Chain Monte Carlo method for Bayesian model updating, model class selection and model averaging. Journal of Engineering Mechanics 133(7), 816-832, 2007

    work page 2007

  49. [49]

    G. S. Fishman. Coordinate selection rules for Gibbs sampling. Univer- sity of North Carolina, UNC/OR TR-92/15, 1996

    work page 1996

  50. [50]

    R. C. Aster, B. Borchers and C. H. Thurber. Parameter Estimation and Inverse Problems. 2nd Edition, Academic Press, 2012

    work page 2012

  51. [51]

    Dashti and A

    M. Dashti and A. M. Stuart. The Bayesian Approach to Inverse Prob- lems. Handbook of Uncertainty Quantification, 1-118. , 2015

    work page 2015

  52. [52]

    Ching and J

    J. Ching and J. Wang. Application of the Transitional Markov Chain Monte Carlo algorithm to probabilistic site characterization. Journal of Engineering Geology 203, 151-167, 2016

    work page 2016

  53. [53]

    J. Wang, L. S. Katafygiotis and M. N. Noori. Transitional Markov Chain Monte Carlo simulation for reliability-based optimization. Safety, Reliability, Risk and Life-Cycle Performance of Structures & Infrastructures – Deodatis, Ellingwood & Frangopol (Eds), 1593-1599, 2014

    work page 2014

  54. [54]

    C. Felippa. Introduction to FEM, FEM Modeling: Mesh, Loads and BCs. Lecture Notes, University of Colorado Boulder, 2016

    work page 2016

  55. [55]

    Adeli, B

    E. Adeli, B. V . Rosi ´c, H. G. Matthies and S. Reinst ¨adler. Bayesian parameter identification in plasticity. XIV International Conference on Computational Plasticity. Fundamentals and Applications COMPLAS XIV E. O˜nate, D.R.J. Owen, D. Peric and M. Chiumenti (Eds), 2017. 18

    work page 2017

  56. [56]

    Effect of Load Path on Parameter Identification for Plasticity Models using Bayesian Methods

    E. Adeli, B. V . Rosi´c, H. G. Matthies and S. Reinst¨adler. Effect of Load Path on Parameter Identification for Plasticity Models using Bayesian Methods. Quantification of Uncertainty: Improving Effieciency and Technology, G. Rozza, M. D’Elia and M. Gunzburger (Eds), http: //arxiv.org/abs/1906.07246, 2018

    work page internal anchor Pith review Pith/arXiv arXiv 1906

  57. [57]

    E. Adeli. Viscoplastic-Damage Model Parameter Identification via Bayesian Methods. Ph.D. Dissertation, Institut f ¨ur Wissenschaftliches Rechnen, Technische Universit¨at Braunschweig, 2019

    work page 2019

  58. [58]

    Gelman, G

    A. Gelman, G. O. Roberts and W. R. Gilks. Efficient Metropolis Jump- ing Rules. In: J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith (ed.), Bayesian Statistics 5, Oxford University Press, 599-607, 1996. 19

    work page 1996