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<p>In response to the static/dynamic loading challenges faced by bolt support in deep engineering, a generalized macroscopic constitutive model suitable for Negative Poisson’s Ratio (NPR) bolts has been developed. This model integrates a generalized hardening law with the Mises yield criterion and an associated flow rule to simulate both yield and post-yield responses under a wide range of loading conditions. To facilitate numerical implementation, a subroutine was embedded into the ABAQUS environment. The model’s performance was validated against experimental results from high-temperature quasi-static (25–600&#xa0;°C) and high strain-rate dynamic (0.1–1000&#xa0;s<sup>−1</sup>) tensile tests, demonstrating excellent agreement with Pearson correlation coefficients exceeding 0.9984. Additionally, the Akaike Information Criterion (AIC) was employed to benchmark the model’s predictive efficiency and parameter compactness against existing formulations, revealing a superior balance between accuracy and simplicity. Sensitivity analysis indicated that the elastic modulus (E) and hardening coefficient (B) are the primary factors influencing yield strength and hardening rate, accounting for 81.47% and 17.62% of the variation, respectively, while parameter A exhibited only a marginal effect (0.91%). Furthermore, the proposed model was applied to an engineering case of roadway support subjected to blast loading in Lingbao City, Henan Province, China. The numerical simulation results showed good agreement with field monitoring data, providing a reliable theoretical tool for the performance evaluation and optimization design of NPR bolts in scenarios such as rockburst protection and anti-blast design.</p>

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Generalized Macroscopic Constitutive Model for NPR Bolts Under Static/Dynamic Loading and Its Application in Deep Underground Roadway Support

  • 期刊论文

  • 发表日期：

    2026年3月11日

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  • Cheng Jiang,
  • Kailong Wu,
  • Yubing Gao,
  • Manchao He,
  • Xingxing Zhang,
  • Long Yuan

摘要

In response to the static/dynamic loading challenges faced by bolt support in deep engineering, a generalized macroscopic constitutive model suitable for Negative Poisson’s Ratio (NPR) bolts has been developed. This model integrates a generalized hardening law with the Mises yield criterion and an associated flow rule to simulate both yield and post-yield responses under a wide range of loading conditions. To facilitate numerical implementation, a subroutine was embedded into the ABAQUS environment. The model’s performance was validated against experimental results from high-temperature quasi-static (25–600 °C) and high strain-rate dynamic (0.1–1000 s−1) tensile tests, demonstrating excellent agreement with Pearson correlation coefficients exceeding 0.9984. Additionally, the Akaike Information Criterion (AIC) was employed to benchmark the model’s predictive efficiency and parameter compactness against existing formulations, revealing a superior balance between accuracy and simplicity. Sensitivity analysis indicated that the elastic modulus (E) and hardening coefficient (B) are the primary factors influencing yield strength and hardening rate, accounting for 81.47% and 17.62% of the variation, respectively, while parameter A exhibited only a marginal effect (0.91%). Furthermore, the proposed model was applied to an engineering case of roadway support subjected to blast loading in Lingbao City, Henan Province, China. The numerical simulation results showed good agreement with field monitoring data, providing a reliable theoretical tool for the performance evaluation and optimization design of NPR bolts in scenarios such as rockburst protection and anti-blast design.