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基于人工神经网络的固体推进剂细观损伤与宏观刚度映射关系

张滔韬 杨玉新 张二晗 校金友 吕海宝 文立华 雷鸣 侯晓

张滔韬, 杨玉新, 张二晗, 等. 基于人工神经网络的固体推进剂细观损伤与宏观刚度映射关系[J]. 复合材料学报, 2024, 42(0): 1-13.
引用本文: 张滔韬, 杨玉新, 张二晗, 等. 基于人工神经网络的固体推进剂细观损伤与宏观刚度映射关系[J]. 复合材料学报, 2024, 42(0): 1-13.
ZHANG Taotao, YANG Yuxin, ZHANG Erhan, et al. Artificial neural network-based mapping of microscopic damage to macroscopic stiffness in solid propellants[J]. Acta Materiae Compositae Sinica.
Citation: ZHANG Taotao, YANG Yuxin, ZHANG Erhan, et al. Artificial neural network-based mapping of microscopic damage to macroscopic stiffness in solid propellants[J]. Acta Materiae Compositae Sinica.

基于人工神经网络的固体推进剂细观损伤与宏观刚度映射关系

基金项目: 国家自然科学基金-联合基金资助项目:高装填比高能推进剂装药结构损伤的跨尺度分析 (U22B20131)
详细信息
    通讯作者:

    雷鸣,博士,副教授,硕士生导师,研究方向为复合材料力学 E-mail: leiming@nwpu.edu.cn

  • 中图分类号: TB332

Artificial neural network-based mapping of microscopic damage to macroscopic stiffness in solid propellants

Funds: Project Cross Scale Analysis of Structural Damage to High Charge Ratio Energetic Propellant Charges (U22B20131) supported by National Natural Science Foundation of China - Joint Fund
  • 摘要: 作为一种高夹杂比颗粒增强聚合物基复合材料,固体推进剂的宏观力学性能主要由其细观结构决定。外加载荷下,初始缺陷或细观颗粒团聚均可诱发局部应力集中,导致颗粒-基体细观界面脱粘,材料宏观力学性能劣化。如何构建细观损伤与宏观性能间的映射关系,已成为推进剂细观实验结果合理运用、固体火箭发动机结构灾变准确预报的关键。为此,本文发展了基于连续介质力学框架的人工神经网络,以变形梯度的不变量为输入、自由能为输出,遴选现有自由能函数和损伤增长函数形式为神经网络设计激活函数,使神经网络先验地满足变形连续性、坐标不变性、热力学一致性等要求。基于上述物理相容性,神经网络能在稀疏训练数据条件下快速收敛,还能够自下而上地实现损伤状态的遗传映射。最后,采用有限元分析获取的数据集,验证了该网络模型对不同预损伤下的推进剂在单轴拉伸、等双轴拉伸、纯剪切三种加载条件下的宏观刚度预报能力。

     

  • 图  1  固体推进剂细观脱粘机理:(a)固体推进剂微观结构SEM图像;(b)无量纲裂纹长度$ \bar l = {\raise0.7 ex\hbox{$l$} \mathord{\left/ {\vphantom {l d}}\right.} \lower0.7 ex\hbox{$d$}} $[10]

    Figure  1.  Microscopic debonding mechanism of solid propellants: (a) SEM image of solid propellants microstructure; (b) Dimensionless crack length $ \bar l = {\raise0.7 ex\hbox{$l$} \mathord{\left/ {\vphantom {l d}}\right.} \lower0.7 ex\hbox{$d$}} $[10]

    图  2  55 vol%颗粒增强粘合剂基体复合材料代表性体积元(RVE)模型及其在三种变形下的仿真应力云图,应力计量对基体剪切模量${\mu _{\text{m}}}$进行归一化

    Figure  2.  Geometry model and simulation stress clouds under three different deformations for the representative volume element (RVE) of 55 vol% particle reinforced binder matrix composite with stress metrology normalized to the matrix shear modulus ${\mu _{\text{m}}}$

    图  3  数值仿真获取的55 vol%颗粒增强粘合剂基体复合材料RVE在单轴拉伸(UT)、等双轴拉伸(ET)、纯剪切(PS)下的2方向应力应变曲线,RVE中有50%区域脱粘(即$\bar l = 0.50$)

    Figure  3.  The 2-directional stress-strain curves obtained by numerical simulation of 55 vol% particle-reinforced binder matrix composites RVE under uniaxial tensile (UT), equibiaxial tensile (ET), and pure shear (PS), with 50% region of debonding in RVE (i.e. $\bar l = 0.50$)

    图  4  数值仿真获取的不同程度损伤下55 vol%颗粒增强粘合剂基体复合材料RVE的弹性模量(2方向)(${E_2}$)、体积模量($K$)、剪切模量($G$)散点图

    Figure  4.  Scatter plots of Young's modulus (2-direction) (${E_2}$), bulk modulus ($K$), and shear modulus ($G$) of 55 vol% particle-reinforced binder matrix composites RVE under different levels of damage obtained by numerical simulation

    图  5  含损伤力学本构神经网络训练框架(以变形梯度${\boldsymbol{F}}$和无量纲裂纹长度$\bar l$为输入,名义应力${\boldsymbol{P}}({\boldsymbol{F}},\bar l)$为输出。其中,力学本构神经网络部分以变形梯度${\boldsymbol{F}}$的不变量${\bar I_1}$、${\bar I_2}$、$J$为输入,输出标量自由能函数$\psi ({\boldsymbol{F}})$;损伤折减神经网络部分以无量纲裂纹长度$\bar l$为输入,输出损伤变量$L(\bar l)$。各隐藏层节点设置可训练权重$ {w_{m,n}} $,$m$为单个网络中的隐藏层编号,$n$为隐藏层中的节点编号;$ {f}_{n}(·) $为激活函数,$n$不同则函数不同)

    Figure  5.  Damage-containing constitutive neural network training framework with deformation gradient ${\boldsymbol{F}}$ and dimensionless crack length $\bar l$ as inputs and nominal stress ${\boldsymbol{P}}({\boldsymbol{F}},\bar l)$ as output (In this framework, the Constitutive neural network part inputs invariant deviation ${\bar I_1}$, ${\bar I_2}$, $J$ of deformation gradient ${\boldsymbol{F}}$,outputs the scalar free energy function $\psi ({\boldsymbol{F}})$. The damage neural network part inputs the dimensionless crack lengths $\bar l$, and outputs the damage variables $L(\bar l)$. Each hidden layer node is set with trainable weights $ {w_{m,n}} $, $m$ is the number of hidden layers in a single network and $n$ is the number of nodes in the hidden layer. $ {f}_{i}(·) $ is the activation function, which is different for different $i$)

    图  6  基于变形梯度不变量、自由能的力学本构神经网络训练框架(采用不变量偏差$[{\bar I_1} - 3]$、$[{\bar I_2} - 3]$、$[J - 1]$作为隐藏层的输入变量,第一层隐藏层以线性$ {(·)}^{1} $、二次函数$ {(·)}^{2} $作为激活函数,第二层以恒等函数$ (·) $和指数函数$ (\mathrm{exp}(·)-1) $作为激活函数)

    Figure  6.  Constitutive neural network training framework based on deformation gradient invariants, free energy theory (The invariant deviations $[{\bar I_1} - 3]$, $[{\bar I_2} - 3]$, $[J - 1]$ are used as the input variables of the hidden layer, the first hidden layer uses linear function $ {(·)}^{1} $ , quadratic function $ {(·)}^{2} $ as the activation function, and the second hidden layer uses the identity $ (·) $ and exponential function $ (\mathrm{exp}(·)-1) $ as the activation function)

    图  7  激活函数选择:(a)线性函数;(b)二次函数;(c)线性指数函数;(d)二次指数函数

    Figure  7.  Activation function selection: (a) Linear; (b) Quadratic; (c) Linear exponential; (d) Quadratic exponential

    图  8  基于Boltzmann生长函数的损伤折减神经网络训练框架(单节点传播结构,以线性函数$ ((·)-1) $和$ \text{Sigmiod}(·) $作为激活函数)

    Figure  8.  Damage neural network training framework based on Boltzmann growth function (Single node propagation structure with linear function $ ((·)-1) $ and $ \text{Sigmiod}(·) $ as activation functions)

    图  9  以单一变形数据作训练集,力学本构神经网络模型对未损伤RVE在UT/ET/PS下应力-变形关系的预测结果(其中${R^2}$为预测评估数,${R^2} = 1.00$表示基本吻合)

    Figure  9.  Prediction of stress-deformation relationship of undamaged RVE under UT/ET/PS by constitutive neural network model using single deformation data as training set (Where ${R^2}$ is the number of predicted evaluations, and ${R^2} = 1.00$ indicates substantial agreement)

    图  10  以UT、BT、PS三种变形数据作训练集,力学本构神经网络模型对未损伤RVE在UT/ET/PS下应力-变形关系的预测结果

    Figure  10.  Prediction results of stress-deformation relationship for undamaged RVE under UT/ET/PS by constitutive neural network model using three kinds of deformation data(UT, BT, and PS)as the training set

    图  11  损伤折减神经网络模型对RVE在UT/ET/PS下脱粘程度$\bar l$与损伤变量$L(\bar l)$映射关系的预测结果

    Figure  11.  Prediction results of damage neural network model for mapping the degree of particle debonding $\bar l$ to damage variables $L(\bar l)$ of the RVE under UT/ET/PS

    图  12  损伤折减神经网络模型对RVE模量${E_2}$/$K$/$G$随$\bar l$劣化的预测结果

    Figure  12.  Predictions of modulus ${E_2}$/$K$/$G$ degradation with $\bar l$ for the RVE by damage neural network model

    图  13  损伤本构神经网络模型对损伤为$\bar l = 0.50$的RVE在UT/ET/PS下的应力-变形关系预测结果

    Figure  13.  Predictions of the stress-deformation relationship for the RVE with damage of $\bar l = 0.50$ under UT/ET/PS by the damage-containing constitutive neural network model

    图  14  损伤本构神经网络模型对损伤为$\bar l = 0.25$和$\bar l = 0.75$的RVE在UT/ET/PS下的应力-变形关系预测结果

    Figure  14.  Predictions of the stress-deformation relationship for the RVE with damage of $\bar l = 0.25$ and $\bar l = 0.75$ under UT/ET/PS by the damage-containing constitutive neural network model

    图  15  RVE在损伤为$\bar l = 0.25$、$\bar l = 0.50$和$\bar l = 0.75$下的UT仿真应力云图

    Figure  15.  UT simulation stress clouds of the RVE at damage of $\bar l = 0.25$,$\bar l = 0.50$and$\bar l = 0.75$

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  • 收稿日期:  2024-02-18
  • 修回日期:  2024-03-28
  • 录用日期:  2024-04-12
  • 网络出版日期:  2024-05-06

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