Identification of Viscoelastic Constitutive Parameters of Acrylic Thin Plates Using Complex Virtual Fields Method

doi:10.12382/bgxb.2024.0051

Abstract

Abstract:

To investigate new methods in the field of material parameter inversion,a complex virtual fields method is proposed for solving the elastic constants of orthogonal anisotropic composite materials.To lay the groundwork for the inversion of orthogonal anisotropic constitutive parameters,an isotropic material,polymethyl methacrylate (PMMA),is initially used as an experimental specimen.Based on thin plate theory and deflectometry,a vibration loading test is conducted on a thin plate specimen to acquire the full-field deformation of the specimen surface.The measured deformation field is processed using C³ continuity Hermite finite elements,resulting in the out-of-plane displacement and curvature fields of the thin plate specimen.The complex virtual fields method is then used to calculate the viscoelastic constants of material.The inversion results are compared with the elastic parameters measured by the three-point bending test and the damping coefficients measured by the cantilever beam hammer impact test.The experimental results show that the measured errors of the elastic modulus and damping coefficients are all within 0.3%.This confirms the feasibility of the proposed method in the inversion of isotropic constitutive parameters and lays the foundation for the subsequent inversion of anisotropic material constitutive parameters.

Key words: virtual fields method, deflectometry, digital image correlation, thin plate vibration, viscoelastic constitutive parameter

CLC Number:

O348.9
O329

WANG Gangting, GUO Baoqiao, LIU Han, LUAN Kedi, GU Yuansen, CHEN Pengwan, ZHOU Jiangfan, LIU Zhanwei. Identification of Viscoelastic Constitutive Parameters of Acrylic Thin Plates Using Complex Virtual Fields Method[J]. Acta Armamentarii, 2025, 46(2): 240051-.

Figures/Tables 24

Fig.1 Kelvin-Voigt viscoelastic model

Fig.2 Experimental set-up of three-point bending

Fig.3 Load-displacement curve for PMMA in three-point bending

Table 1 Elastic modulus parameters of PMMA

样本	弹性模量E_f/MPa
1	1904
2	1908
3	1906
4	1903
均值	1905
均方差	2.2

Fig.4 Schematic diagram of damping device

Table 2 Damping parameters of PMMA

样本	阻尼参数ζ
1	0.0356
2	0.0344
3	0.0348
4	0.0342
5	0.0357
均值	0.0349
标准差	0.0006

Fig.5 Schematic diagram of deflectometry

Fig.6 Schematic diagram of specimen dimensions

Fig.7 Relevant calculation area and mirror reflection effect of thin plate

Fig.8 Vibration loading experimental platform

Fig.9 Schematic diagram of vibration synchronization

Fig.10 Slope fields at 50Hz

Fig.11 Slope fields at 150Hz

Fig.12 Slope fields at 200Hz

Fig.13 Slope fields at 500Hz

Fig.14 Slope fields at 800Hz

Fig.15 Slope fields at 1000Hz

Fig.16 Schematic diagram of rectangular Hermite finite element

Fig.17 3×3 Hermite finite element mesh

Fig.18 Deformation fields of reconstructed PMMA thin plate at 1000Hz frequency

Fig.19 Reconstructed images of 4 sets of virtual deformation fields

Table 3 Four sets of inverted viscoelastic constitutive parameters

样本	频率/Hz	E₁₁/Gpa	E₂₂/Gpa	ν₁₂	G₁₂/Gpa
1	50	1.900	1.906	0.358	0.701
2	150	1.905	1.900	0.357	0.701
3	200	1.910	1.912	0.361	0.702
4	500	1.898	1.898	0.355	0.700
5	800	1.902	1.907	0.364	0.698
6	1000	1.903	1.904	0.350	0.705
均值	-	1.905	1.906	0.358	0.700
标准差	-	0.002	0.002	0.005	0.003

Table 4 Inverted damping parameters for the virtual fields method

样本	η₁₁	η₂₂
1	0.0342	0.0345
2	0.0346	0.0348
3	0.0352	0.0343
4	0.0343	0.0350
5	0.0348	0.0352
6	0.0351	0.0347
均值	0.0349	0.0348
标准差	0.0003	0.0005

Table 5 Comparison of the results obtained by complex virtual fields method and the reference results

样本	弹性模量/GPa	阻尼
反演参数	1.9055	0.0348
实验	1.9052	0.0349
相对误差/%	0.016	0.29

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