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耦合各向异性损伤粘塑性本构模型的一种简单数值实现方法
A Simple Numerical Implementation Method for Anisotropic Damage Coupled Viscoplastic Constitutive Model
投稿时间:2024-01-29  修订日期:2024-03-06
DOI:
中文关键词:  各向异性损伤  粘塑性本构模型  数值实现  径向返回算法  有限元法
英文关键词:Anisotropic damage  Viscoplastic constitutive model  Numerical implementation  Radial return algorithm  Finite element method
基金项目:国家重点研发计划资助项目(2022YFB4100403)
作者单位邮编
王元良 华北电力大学 102206
李昌硕 华北电力大学 
徐鸿 华北电力大学 
朱忠亮 华北电力大学 
倪永中* 华北电力大学 102206
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中文摘要:
      针对耦合Lemaitre各向异性损伤理论的Chaboche型粘塑性本构模型提出了一种简单的数值实现方法。使用解耦的算法,在每个增量步开始时基于向前差分格式更新损伤张量,并在本构方程离散化的过程中将其视作常量。基于应变等效假设,在有效偏应力空间中构建只含有偏张量的方程,将径向返回过程简化为求解一个关于累积塑性应变增量的非线性标量方程。基于voigt表记法格式给出了数值实现方法及一致切线算子的推导过程。在单轴和多轴应力状态下与实验数据和各向同性标量损伤模型模拟结果之间的对比验证了该方法的有效性与高计算效率,不同时间步长下的数值结果也表明该方法具有较好的准确性和稳定性。
英文摘要:
      A simple numerical implementation method is proposed for the Chaboche-type viscoplastic constitutive model coupled with Lemaitre anisotropic damage theory. Using the decoupled algorithm, the damage tensor is updated based on the forward difference format at the beginning of each incremental step. The damage tensor is considered as a constant in the discretization process of constitutive equations. Based on the hypothesis of strain equivalence, the formulations containing only partial tensors are constructed in the effective deviatoric stress space, and the radial return process is simplified to solve a nonlinear scalar equation concerning the accumulated plastic strain increment. The numerical implementation method and the derivation of consistent tangent operator are provided based on the Voigt notation scheme. The comparison between the experimental data and the simulation results of isotropic scalar damage model under uniaxial and multiaxial stress states validates the effectiveness and high computational efficiency of this method. Numerical results under different time step sizes also indicate the good accuracy and stability.
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