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A finite strain visco-hyperelastic damage model for rubber-like materials: theory and numerical implementation

橡胶类材料有限变形黏-超弹性损伤模型: 理论和数值实现

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Abstract

Many rubber-like materials exhibit hyperelastic, time-dependent, rate-dependent and progressive damage behaviors. In our previous work (Lu et al., 2020), we proposed a hyperelastic damage model to characterize the strain-softening behavior of soft materials. The model modifies the strain energy function of a single chain by introducing an internal damage variable D and then maps the deformation of chains to the macroscopic deformation. In this work, we extend this model to incorporate the time-dependent viscous effect using the Prony series-based nonlinear theory. We further implement the finite strain visco-hyperelastic damage model into finite element software ABAQUS by a user material subroutine UMAT. We use the experimental data of a kind of acrylic polymer under uniaxial tension in literature to calibrate the model parameters, including 4 time-independent parameters and 6 time-dependent parameters. We then use the calibrated parameters to simulate the uniaxial tension and stress relaxation of the acrylic polymer specimen with a complex geometry. The simulated results agree with the experimental data with a remarkable accuracy.

摘要

橡胶类材料存在着超弹性、时间相关性、率相关性和渐进损伤行为. 作者之前的工作提出了一种超弹性损伤模型去描述软材料的应变软化行为(Lu et al., 2020). 模型在单根分子链应变能函数中引入损伤变量D, 然后将宏观变形和单链分子的伸长率联系在一起. 本文改进了之前的模型, 通过引入以Prony级数为基础的非线性黏弹性理论使得模型可以表征时间相关黏性效应. 本文进一步将建立的有限变形黏-超弹性损伤本构模型在有限元软件ABAQUS中通过用户自定义子程序UMAT实现. 本文利用文献中丙烯酸聚合物在单轴拉伸下的实验数据来校准本构模型的10个参数: 包括4个弹性参数和6个黏性参数. 利用ABAQUS模拟丙烯酸聚合物复杂几何形状试样的单轴拉伸和应力松弛, 仿真结果与实验数据一致性较好.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11922210).

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Authors and Affiliations

  1. State Key Lab for Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics, Xi’an Jiaotong University, Xi’an, 710049, China

    Zhenjiang Du  (杜振江), Yan Yang  (杨彦) & Tongqing Lu  (卢同庆)

  2. Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, 14853, USA

    Zhongtong Wang  (王仲彤)

  3. Navigation and Control Technology Research Institute of China North Industries Group Corporation, Beijing, 100089, China

    Xinggui Fan  (范兴贵)

Authors
  1. Zhenjiang Du  (杜振江)
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  2. Yan Yang  (杨彦)
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  3. Zhongtong Wang  (王仲彤)
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  4. Xinggui Fan  (范兴贵)
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  5. Tongqing Lu  (卢同庆)
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Contributions

Zhenjiang Du created the constitutive model, achieved the UMAT, processed the numerical simulations and wrote the first draft of the manuscript. Yang Yan, Zhongtong Wang and Xinggui Fan revised the final version. Tongqing Lu supervised the whole project and revised the manuscript.

Corresponding author

Correspondence to Tongqing Lu  (卢同庆).

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Du, Z., Yang, Y., Wang, Z. et al. A finite strain visco-hyperelastic damage model for rubber-like materials: theory and numerical implementation. Acta Mech. Sin. 39, 222473 (2023). https://doi.org/10.1007/s10409-023-22473-x

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