橡胶类材料有限变形黏-超弹性损伤模型:理论和数值实现  

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

作　　者：杜振江 杨彦 王仲彤 范兴贵 卢同庆 Zhenjiang Du;Yan Yang;Zhongtong Wang;Xinggui Fan;Tongqing Lu(State Key Lab for Strength and Vbration of Mechanical Structures,DeparmentofEngineering Mechanics,Xi'an Jiaoong University Xi'an710049,China;Sibley School of Mechanical and Aerospace Engineering,Cornell University,Iihaca 14853,United Siates;Navigation and Control Technology Research Institute of China North Industries Group Corporation,Beijing 100089,China)

机构地区：[1]State Key Lab for Strength and Vbration of Mechanical Structures,DeparmentofEngineering Mechanics,Xi'an Jiaoong University Xi'an710049,China [2]Sibley School of Mechanical and Aerospace Engineering,Cornell University,Iihaca 14853,United Siates [3]Navigation and Control Technology Research Institute of China North Industries Group Corporation,Beijing 100089,China

出　　处：《Acta Mechanica Sinica》2023年第3期56-63,共8页力学学报（英文版）

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

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.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.

关 键 词：Soft materials HYPERELASTIC VISCOELASTIC DAMAGE UMAT 

分 类 号：TQ33[化学工程—橡胶工业]