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Determination of the parameters of a material constitutive relation using the surrogate model along with dynamic indentation test
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  • Published: 16 February 2026

Determination of the parameters of a material constitutive relation using the surrogate model along with dynamic indentation test

  • G. H. Majzoobi1 &
  • S. Pourolajal1 

Scientific Reports , Article number:  (2026) Cite this article

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We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Engineering
  • Materials science

Abstract

It is well-known that materials behavior changes with strain rate and temperature. The changes are described by an equation known as material model. The model involves a number of constants which are normally determined by experiment. In this study, the constants of Zerilli-Armstrong model are identified using dynamic indentation test combined with numerical simulation and an optimization technique. The specimens made of a steel alloy are subjected to indentation tests at four different strain rates and four temperatures and the experimental load-depth curve is recorded. The dynamic indentation test is simulated using Ls-dyna hydro code and the numerical load-depth is obtained. Attempts are made to optimize the error between the experimental and the numerical load-depth curves. This is accomplished using Surrogate model. The results are validated using the stress–strain curves obtained from Hopkinson bar tests. The study shows that the method yields acceptable results. The results obtained using artificial neural network and optimization technique, based on a quadratic polynomial, which have been reported in the previous works for Johnson–Cook model are reproduced here for Zerilli-Armstrong model for comparison purposes.

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Data availability

All data generated or analysed during this study are included in this published article.

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Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Engineering Faculty, Bu-Ali Sina University, Hamedan, Iran

    G. H. Majzoobi & S. Pourolajal

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  1. G. H. Majzoobi
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  2. S. Pourolajal
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Contributions

S.P. was my Phd student and has done the experiments, prepared the figures and tables. G.H.M. was the supervisor of S.P. He has supervised the thesis and written the paper.

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Correspondence to G. H. Majzoobi.

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Cite this article

Majzoobi, G.H., Pourolajal, S. Determination of the parameters of a material constitutive relation using the surrogate model along with dynamic indentation test. Sci Rep (2026). https://doi.org/10.1038/s41598-025-06192-6

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  • Received: 17 October 2024

  • Accepted: 06 June 2025

  • Published: 16 February 2026

  • DOI: https://doi.org/10.1038/s41598-025-06192-6

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Keywords

  • Dynamic indentation test
  • Strain rate
  • Quadratic polynomial
  • Surrogate model
  • Artificial neural network
  • Temperature
  • Zerilli-Armstrong model
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