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A modeling method for elastic-viscous-plastic material with fractal structure and its solution

一种具有分形结构的弹黏塑性材料建模及其求解方法

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Abstract

A modeling method with the fractal structure to describe the elastic-viscous-plastic properties of materials is proposed in this paper. Moreover, the solution can be obtained without solving the corresponding infinite order differential equation. Then, a model (L-R model) to characterize the elastic-viscous-plastic properties of materials with complex infinite order fractal structure was established based on this modeling method. The mechanical properties are described by the constitutive relationship of spring (elasticity), adhesive pot (viscosity), and plastic body (plasticity) elements by MATLAB/Simulink. The three-element model is connected in series and parallel according to the rules of the Bingham model. Then, the Bingham model is used as the original model to set and iterate according to the fractal theory. And the solution of the corresponding infinite order differential equation for describing elastic-viscous-plastic of materials can be obtained directly without solving the complex differential equation of the model. To verify the reliability of this modeling method and its solution results, cyclic load experiments were carried out on five materials with different fractal structures, steel, slate, coal, red sandstone, and salt rock. Comparing the experimental results with the solution results, it indicated that the established model can effectively describe the material’s performance of the elastic-viscous-plastic properties.

摘要

本文建立了一种具有分形结构的元件模型, 用于描述材料弹粘塑性特性, 并可以在无需求解相应的无限阶微分方程的情况下获得各载荷作用下模型的力学反应. 首先, 基于这种建模方法, 建立了表征具有复杂无限阶分形结构材料弹黏塑性特性的混联元件模型(L-R模型). 然后, 利用MATLAB/Simulink, 借助弹簧(弹性)、 黏壶(黏性)和塑性体(塑性)单元的本构关系来描述材料的基本力学性能. 之后, 将宾厄姆模型作为基本模型按照分形理论进行迭代, 通过求解得到描述材料在各种载荷作用下的力学(弹黏塑性)反应. 最后, 为了验证该建模方法及其求解结果的可靠性, 在钢、 板岩、 煤、 红砂岩和盐岩五种不同分形结构的材料上进行了循环载荷实验. 将实验结果与求解结果进行比较, 表明所建立的模型能够有效地描述材料的弹黏塑性性能.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grant No. 41572334), and the Innovation Fund Research Project (Grant Nos. SKLGDUEK202222 and SKLGDUEK202216).

Author information

Authors and Affiliations

  1. State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing, 100083, China

    Dejian Li  (李德建), Hao Qi  (祁浩), Mingyuan Zhang  (张鸣原), Junhao Huo  (霍君豪) & Yuanhao Rao  (饶远昊)

  2. Institute for Deep Underground Science and Engineering, Beijing, 100083, China

    Dejian Li  (李德建), Hao Qi  (祁浩), Mingyuan Zhang  (张鸣原) & Junhao Huo  (霍君豪)

  3. School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing, 100083, China

    Dejian Li  (李德建), Hao Qi  (祁浩), Mingyuan Zhang  (张鸣原), Junhao Huo  (霍君豪) & Jiangshuo Liu  (刘江硕)

  4. China Academy of Urban Planning and Design, Beijing, 100044, China

    Yuanhao Rao  (饶远昊)

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  1. Dejian Li  (李德建)
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  2. Hao Qi  (祁浩)
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Contributions

Author contributions Dejian Li proposed the idea, set the research target (Conceptualization), developed the modeling method (Methodology), and acquired the funding, i.e., the National Natural Science Foundation of China (Grant No. 41572334) and the Innovation Fund Research Project (Grant No. SKLGDUEK202222) (Funding acquisition). Hao Qi produced metadata (Data curation), conducted formal analysis (Formal analysis), and conducted the series experiments (Investigation). Mingyuan Zhang conducted data analysis and designed the methodology of the study (Formal analysis and Methodology), acquired the funding, i.e., the Innovation Fund Research Project (Grant No. SKLGDUEK2022016), and wrote the original draft and edited it. Junhao Huo conducted computational analysis (Formal analysis), and drew figures (Visualization). Jiangshuo Liu checked the data in the manuscript and reviewed the paper (Validation). Yuanhao Rao conducted the series experiments (Investigation), proposed the new model (Methodology), and produced metadata and scrub data (Data curation).

Corresponding authors

Correspondence to Dejian Li  (李德建), Mingyuan Zhang  (张鸣原) or Yuanhao Rao  (饶远昊).

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Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Li, D., Qi, H., Zhang, M. et al. A modeling method for elastic-viscous-plastic material with fractal structure and its solution. Acta Mech. Sin. 40, 423263 (2024). https://doi.org/10.1007/s10409-023-23263-x

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