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<p>Inverse engineering (IE) techniques have increasingly been adopted in engineering disciplines to identify input parameters that reproduce desired system responses. Unlike conventional forward problems, IE focuses on deducing the governing variables from known outputs. In this study, an inverse engineering framework based on the multi-level response surface method (MLRSM) is proposed for the calibration of constitutive models. This methodology first obtains preliminary Johnson–Cook (J–C) parameters using Bridgman’s method. Subsequently, a design of experiments is generated through finite element (FE) simulations. The number of simulation runs is based on the number of parameters and the required detail of the response functions. Throughout the process, surrogate models are developed at each level to estimate the error between the simulation outputs and the reference data. An iterative optimization scheme is applied to minimize this deviation under the imposed constraints. The proposed MLRSM-based IE approach significantly enhances calibration accuracy, achieving more than a twofold improvement compared to the initial estimates. The results demonstrate that the method provides a robust and efficient pathway for identifying J–C constants in tensile testing, with potential applicability to other constitutive models and complex loading scenarios. While the discrepancy between simulated and experimental results for a standard tensile specimen is only 1.06%, larger errors are observed for specimens with grooves.</p>

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Inverse Engineering Framework Based on Multi-level Response Surface Method for Accurate Calibration of Johnson–Cook Constitutive Model

  • 期刊论文

  • 发表日期：

    2026年4月17日

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  • Seyyed Ehsan Eftekhari Shahri,
  • Sadegh Ranjbar,
  • Masoud Rakhshkhorshid,
  • Mahmoud Afshari

摘要

Inverse engineering (IE) techniques have increasingly been adopted in engineering disciplines to identify input parameters that reproduce desired system responses. Unlike conventional forward problems, IE focuses on deducing the governing variables from known outputs. In this study, an inverse engineering framework based on the multi-level response surface method (MLRSM) is proposed for the calibration of constitutive models. This methodology first obtains preliminary Johnson–Cook (J–C) parameters using Bridgman’s method. Subsequently, a design of experiments is generated through finite element (FE) simulations. The number of simulation runs is based on the number of parameters and the required detail of the response functions. Throughout the process, surrogate models are developed at each level to estimate the error between the simulation outputs and the reference data. An iterative optimization scheme is applied to minimize this deviation under the imposed constraints. The proposed MLRSM-based IE approach significantly enhances calibration accuracy, achieving more than a twofold improvement compared to the initial estimates. The results demonstrate that the method provides a robust and efficient pathway for identifying J–C constants in tensile testing, with potential applicability to other constitutive models and complex loading scenarios. While the discrepancy between simulated and experimental results for a standard tensile specimen is only 1.06%, larger errors are observed for specimens with grooves.