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A simplified calculation of the specimen’s stress-strain curve is generally conducted using the two-wave method by the split Hopkinson pressure bar (SHPB), which aligns the onset of the transmitted and reflected waves. However, this approach neglects the travel time of elastic waves within the specimen. Considering the travel time of elastic waves, this study quantitatively investigates the error characteristics and patterns of stress, strain, and strain rate in the specimen under different conditions using the theoretical two-wave method, and compares the results with those obtained using the onset-aligned two-wave method. The study reveals that the stress-time curves derived from the theoretical two-wave method are lower than the actual stress curves, whereas those obtained from the onset-aligned two-wave method are consistently higher than the actual stress curves, with the stress deviation approximating a constant value when the dimensionless time exceeds 2.0. The starting point of the stress-strain curves obtained by the theoretical two-wave method is not zero but a point on the strain axis, whereas the onset-aligned two-wave method always starts at zero. However, the slopes of the stress-strain curves obtained by both methods differ from the actual Young’s modulus of the material, and functional relationships between the slopes and the actual Young’s modulus are provided. This research offers theoretical guidance for the refined design of SHPB experiments and the accurate processing of data. [ABSTRACT FROM AUTHOR]

• In-depth wave propagation Analysis: conducted a comprehensive analysis of elastic wave transmission and reflection in specimens, considering different incident waveforms and specimen dimensions. • Numerical simulation Validation: employed numerical simulations to validate theoretical models, ensuring accuracy in predicting stress wave behavior in SHPB experiments. • Parameter influence Study: extensively analyzed the impact of experimental variables like wave impedance, specimen material density, and incident wave characteristics on stress-strain response, enhancing the understanding of material behavior in dynamic testing. In Split Hopkinson Pressure Bar (SHPB) tests, the stress wave effects during the elastic phase of the stress-strain curve and their influence mechanisms are crucial. Due to the extremely short duration of the elastic deformation phase, the stress wave effects on the specimen during this stage cannot be ignored. This leads to significant errors in the obtained elastic stress-strain curves. However, the dynamic compressive elastic stress-strain relationship forms the basis for studying the viscoelastic behavior of materials. Accurate determination of elastic yield stress and yield strain is also essential for deriving accurate plastic stress-strain relationships. Quantitative research on the stress wave effects during the elastic compression phase of SHPB tests is fundamental for decoupling and obtaining accurate material elastic curves. This paper conducts a quantitative theoretical analysis of the structural effects caused by stress wave evolution during the elastic compression phase, based on the assumption of plane waves. It studies the deviation characteristics and main factors of the phenomenological engineering stress-strain curves of the specimen compared to the actual material stress-strain curves under different conditions, revealing the influence rules and mechanisms of this deviation. The maximum stress deviation value and its corresponding dimensionless time, as well as the variation trend of the maximum stress deviation value within different fluctuation intervals, are calculated. Additionally, the study investigates the cases where the incident wave is arc-shaped or a combination of arc and linear waves. The findings provide theoretical references for the precise design and accurate data processing of SHPB tests. [ABSTRACT FROM AUTHOR]

The vertical vibration of a viscoelastic pile immersed in arbitrarily layered soil is investigated by taking the interaction among pile, pile surrounding soil (PSS) and pile end soil (PES) into account. Firstly, considering both the stratification and stress wave effect of soil, a mathematical model of the pile–soil system is established based on the fictitious soil pile (FSP) model. Then, utilizing the impedance function transfer method and Laplace transform technique, the analytical solutions of the vertical dynamic impedance of pile are derived in the frequency domain. The analytical solutions are validated by comparing them with other existing solutions. Finally, a parametric study is put forward to investigate the properties of PES on the vertical dynamic impedance of pile. The results reveal that the properties of PES have a significant effect on the vertical dynamic impedance of pile, but there is a critical influence thickness for this effect. For the cases of the PES thickness exceeding the critical influence thickness, further increase of PES thickness will not affect the dynamic behavior of the pile–soil system. [ABSTRACT FROM AUTHOR]

The vertical vibration of a viscoelastic pile immersed in arbitrarily layered soil is investigated by taking the interaction among pile, pile surrounding soil (PSS) and pile end soil (PES) into account. Firstly, considering both the stratification and stress wave effect of soil, a mathematical model of the pile–soil system is established based on the fictitious soil pile (FSP) model. Then, utilizing the impedance function transfer method and Laplace transform technique, the analytical solutions of the vertical dynamic impedance of pile are derived in the frequency domain. The analytical solutions are validated by comparing them with other existing solutions. Finally, a parametric study is put forward to investigate the properties of PES on the vertical dynamic impedance of pile. The results reveal that the properties of PES have a significant effect on the vertical dynamic impedance of pile, but there is a critical influence thickness for this effect. For the cases of the PES thickness exceeding the critical influence thickness, further increase of PES thickness will not affect the dynamic behavior of the pile–soil system.