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Jan-Eric Ståhl

Jan-Eric Ståhl


Jan-Eric Ståhl

A machine learning based approach for determining the stress-strain relation of grey cast iron from nanoindentation


  • Jian Weng
  • Rebecka Lindvall
  • Kejia Zhuang
  • Jan Eric Ståhl
  • Han Ding
  • Jinming Zhou

Summary, in English

Apart from microhardness and elastic modulus, the stress-strain relation is another important characteristic that more and more scholars have been trying to extract from nanoindentation. With the development of artificial intelligence and computer technology, a machine learning based method is proposed in this paper to extract stress-strain curve of grey cast iron using sharp nanoindentation. Firstly, the average curve is achieved by the grid-design nanoindentation to avoid the influence of different phases on indentation results. The plastic behavior is considered as a power law function in this paper. Then, finite element method supports to generate a simulation data set, with full-factor and full-level design of constants of stress-strain relation. With the simulation data set, the support vector regression machine establishes a surrogate model to correlate the input (constants of stress-strain function) and output (the mean error between predicted and measured results). The best parameters of support vector machine are determined through grid search and cross-validation. PSO serves as the optimization algorithm to find the optimum of input related to the measured results, with an inertia factor to improve the local search ability. Finally, the simulation loading curve with the optimal constants provided by PSO perfectly fits the measured loading curve, which shows the effectiveness of the inverse method proposed in this paper.


  • Production and Materials Engineering
  • NanoLund: Center for Nanoscience
  • SPI: Sustainable Production Initiative

Publishing year





Mechanics of Materials



Document type

Journal article




  • Metallurgy and Metallic Materials


  • Inverse calculation
  • Machine learning
  • Nanoindentation
  • Stress-strain relation




  • ISSN: 0167-6636