Parameter inversion of the polymethyl methacrylate constitutive model based on explosive cutting experiment
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摘要: 为了获取爆炸切割数值模拟中有机玻璃（PMMA）的材料本构模型参数，建立了一种基于神经网络的有机玻璃Johnson Holmquist ceramics (JH-2)本构模型参数反演方法：基于从爆炸切割试验和现有研究得到的JH-2本构模型经验参数，确定本构模型参数的调整区间；使用LS-DYNA数值模拟软件对2.5 mm宽爆炸切割索切割14 mm PMMA平板过程进行数值模拟并收集平板损伤数据集；建立PMMA平板本构模型参数与损伤数据之间的神经网络模型；通过训练完成的神经网络模型对PMMA平板的JH-2本构模型参数进行反演。为验证通过反演参数的可靠性，进行了4.2 mm宽爆炸切割索切割19 mm PMMA平板试验和有限元数值模拟，计算结果中的平板损伤情况与实验结果相差较小，表明通过反演获得的JH-2本构模型参数能较好地应用于PMMA平板爆炸切割数值模拟。传统材料参数获取方法，该参数反演方法相较于可以通过较少的试验及测试，获得比较准确的材料本构模型参数。Abstract: In order to obtain the material constitutive model parameters of polymethyl methacrylate (PMMA) in the numerical simulation of explosive cutting, and to avoid the multiple tests required by the traditional method of obtaining the material constitutive model parameters, a neural network-based inversion method of the Johnson Holmquist Ceramics (JH-2) constitutive model parameters of PMMA was established. Firstly, a 2.5-mm-wide linear shaped charge was used to cut 14 mm PMMA flat plate, and the results of the explosive cutting test were analyzed to classify and quantify the damage of PMMA flat plate into three kinds of damage data: penetration depth, impact fracture thickness and spallation damage thickness. Based on the empirical parameters of the JH-2 constitutive model obtained from the explosive cutting experiments and existing studies, the adjustment interval of the constitutive model parameters was determined. LS-DYNA was used to simulate the process of cutting 14 mm PMMA flat plate with 2.5 mm wide linear shaped charge and to collect a flat plate damage data set containing the three kinds of damage data. A neural network model between the parameters of the PMMA flat plate constitutive model and the damage data was developed, and the model was trained using the plate damage data set. The inversion of the JH-2 constitutive model parameters of the PMMA flat plate was performed by the trained neural network model. In order to verify the reliability of the parameters obtained by the inversion method, a 4.2 mm wide linear shaped charge cutting 19 mm PMMA flat plate experiments and finite element numerical simulation were conducted, and the fracture characteristics and damage data of the PMMA flat plate in the calculation results were less different from the experiment results, indicating that the JH-2 constitutive model parameters obtained by the inversion can be better applied to PMMA flat plate explosive cutting numerical simulation. The parameter inversion method can obtain more accurate material constitutive model parameters with less experiments and tests than the traditional material parameter acquisition method.
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Key words:
- neural network /
- explosive cutting /
- finite element analysis /
- parameter inversion
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图 7 PMMA平板爆炸切割试验数值模拟结果
Figure 7. Numerical simulation results of PMMA flat plate explosive cutting test
图 8 试验结果与数值模拟结果对比
Figure 8. Comparison of test results and numerical simulation results
表 1 冲击强度测试数据
Table 1. Testing data of impact strength
平板 冲击强度/(J·cm−2) 测试1 测试2 测试3 平均值 1 1.35 1.50 1.25 1.37 2 1.83 1.65 1.74 1.74 3 2.85 2.82 3.00 2.89 
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表 2 PMMA平板损伤数据
Table 2. PMMA flat plate damage data
平板 平板厚度/mm 侵彻深度/mm 冲击断裂厚度/mm 层裂厚度/mm 是否成功切开 1 14 3.5 5.5 5.0 是 2 14 4.7 4.8 4.5 是 3 14 7.3 0 0 否
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表 3 PMMA平板JH-2本构模型参数调整区间
Table 3. Adjustment interval of parameters of PMMA flat plate JH-2 constitutive model
A B C M N 1.85～2.05 2.35～2.65 −0.001～0.001 0.50～0.80 0.50～0.80
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表 4 数据集的输入值
Table 4. Input values of the dataset
编号 h1/cm h2/cm h3/cm d1/cm d2/cm d3/cm δ1/cm δ2/cm δ3/cm 1 5.0 2.0 7.0 4.5 3.9 1.4 7.2 1.5 0 2 3.4 4.9 5.7 4.1 4.9 5.0 6.9 3.1 0 … … … … … … … … … … 61 3.3 5.3 5.4 3.2 7.8 3.0 5.2 3.1 0 62 4.1 5.2 4.7 3.5 8.0 2.5 6.0 1.3 0
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表 5 数据集的输出值
Table 5. Output values of the dataset
编号 A B C M N 1 1.92 2.40 0.0035 0.52 0.55 2 1.94 2.47 −0.0021 0.61 0.59 … … … … … … 61 1.99 2.55 −0.0011 0.60 0.55 62 2.03 2.59 0 0.60 0.67
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表 6 PMMA平板JH-2本构模型参数反演值
Table 6. Inversion values of parameters of PMMA flat plate JH-2 constitutive model
A B C M N 1.9566 2.4918 −0.0205 0.5861 0.5860
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表 7 试验结果与数值模拟结果对比
Table 7. Comparison of test results and numerical simulation results
材料 侵彻深度/mm 冲击断裂厚度/mm 层裂厚度/mm 试验 数值模拟 试验 数值模拟 试验 数值模拟 Sample 1 3.5 3.4 5.5 5.5 5.0 5.1 Sample 2 4.7 4.7 4.7 4.7 4.6 4.6 Sample 3 7.3 7.0 0 0 0 0
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