The Meso-scale Modeling Method for Concrete Based on Block Division and Parallel Filling and Its Application in High-speed Penetration

doi:10.12382/bgxb.2023.0945

Abstract

Abstract:

Based on the need for rapid generation of large and complex finite element model in the meso-scale simulation of high-speed deep penetration, a meso-scale modeling method of concrete based on material property identification, block division and parallel filling is proposed. Different interface transition zone (ITZ) characterization methods are used to verify the characterization ability of the meso-scale modeling method under quasi-static and ultra-high speed penetration conditions. The accelerated modeling method has significant advantages in modeling efficiency and accuracy, which can achieve rapid modeling of large and complex shaped concrete structures and precise proportion allocation of microscopic components. Furthermore, the applicable conditions and the initial judgment criteria of material parameters of different ITZ characterization methods (i.e., ITZ solid element method, non-ITZ method and cohesive contact method) are summarized. The ITZ solid element method has the best prediction effect on penetration depth and crater size in ultra-high speed penetration simulation (the deviation is less than 10%); the cohesive contact method has the relatively worst performance in crater size prediction because it does not introduce strain rate effect and is prone to numerical instability. In addition, the response calculation and morphology characterization of the eroded projectile in the meso-scale simulation are highly consistent with the established nose evolution model for high-speed penetration. The research results can solve the difficulties of modeling the large and complex meso-scale targets in engineering practice, and provide the basis for exploring the meso-scale mechanism of ultra-high speed deep penetration.

Key words: meso-scale simulation, parallel acceleration, interface characterization, ultra-high speed penetration

CLC Number:

TU37
E920.8

LI Xu, LIU Yan, YAN Junbo, SHI Zhenqing, WANG Hongfu, XU Yingliang, HUANG Fenglei. The Meso-scale Modeling Method for Concrete Based on Block Division and Parallel Filling and Its Application in High-speed Penetration[J]. Acta Armamentarii, 2023, 44(12): 3543-3561.

Figures/Tables 30

Fig.1 Flow chart of concrete meso-scale modeling method

Table 1 Volume fraction of aggregate with different particle sizes in each formula%

编号	骨料占比/%	粒径分布/mm	骨料粒径范围/mm
编号	骨料占比/%	粒径分布/mm	5~10	10~20	20~40
C_40_10	40	5~10	40
C_40_20	40	5~20	16.6	23.4
C_40_40	40	5~40	9.1	12.8	18.1

Fig.2 Schematic diagram of three-dimensional random polyhedral aggregate

Fig.3 Block division of 3D model of structural specimens

Table 2 Generation efficiency comparison of block division and parallel fillingmeso-scale modeling method (C_40_40)

区块数	CPU数	单元尺寸/mm	T/s	χ
1×1×1	1	0.8	984	1
		1.0	1205	1
		1.5	1381	1
2×2×2	3	0.8	281	3.50
		1.0	365	3.30
		1.5	500	2.76
	5	0.8	224	4.39
		1.0	277	4.35
		1.5	396	3.49
	8	0.8	177	5.56
		1.0	198	6.09
		1.5	293	4.71
3×3×3	3	0.8	336	2.93
		1.0	382	3.15
		1.5	571	2.42
	5	0.8	159	6.19
		1.0	209	5.77
		1.5	445	3.10
	12	0.8	145	6.79
		1.0	183	6.58
		1.5	225	6.14
	27	0.8	103	9.55
		1.0	135	8.93
		1.5	192	7.19

Fig.4 Comparison of normalized computation time and speedup of block division and parallel filling method

Fig.5 Schematic diagram of material property identification in local background grid (2D)

Fig.6 Aggregate and ITZ obtained by solid element method

Fig.7 Meso-scale model of C_40_40 concrete by solid element method

Fig.8 Influences of aggregate gradation and element size on volume fraction of concrete meso components

Table 3 Parameter modification values of K&C model

参数	数值	参数	数值	参数	数值
λ₁	0	η₁	0	a₀	0.4426f_c
λ₂	8.0×10^-6	η₂	0.25	a₁	0.5698
λ₃	2.4×10^-5	η₃	0.62	a₂	0.02516/f_c
λ₄	4.0×10^-5	η₄	0.84	a₀_y	0.2797f_c
λ₅	6.0×10^-5	η₅	0.97	a₁_y	0.8989
λ₆	8.7×10^-5	η₆	1.00	a₂_y	0.0685/f_c
λ₇	2.0×10^-4	η₇	0.83	a_0f	0
λ₈	3.0×10^-4	η₈	0.69	a_1f	0.5698
λ₉	6.0×10^-4	η₉	0.47	a_2f	0.02516/f_c
λ₁₀	1.0×10^-3	η₁₀	0.33
λ₁₁	3.0×10^-3	η₁₁	0.15
λ₁₂	0.01	η₁₂	0.008
λ₁₃	10	η₁₃	0

Table 4 Specimen parameters for quasi-static mechanical test

试验类型	试块尺寸/ mm	试块强度/ MPa	等效强度^a/ MPa	砂浆强度^b/ MPa	骨料强度/ MPa	ITZ强度/ MPa	骨料粒径/ mm	骨料占比/ %	来源
单轴压缩	150×150×150	51.2	51.2	37 (31)	120	19	5~20	40	本文
单轴压缩	100×100×100	48.4	46.0	36 (33)	120	22	4~8	20	文献[36]
三轴压缩	ϕ55.5×110	60.2	68.7	50	150	38	5~14	35	文献[37]
劈裂抗拉	150×150×150	2.38		36	80	28.8	5~40	40	文献[38]

Fig.9 Finite element model for quasi-static mechanical test

Fig.10 Loading rate curve of platen

Fig.11 Comparison of stress-strain curves of uniaxial compression simulation under different end friction conditions

Table 5 Comparison of damage nephograms of uniaxial compression meso-scale simulation under different end friction conditions based on ITZ solid element method

Fig.12 Influences of different ITZ characterization methods on uniaxial compression meso-scale simulation

Fig.13 Stress-strain curves of meso-scale simulation of triaxial compression at different confining pressures

Table 6 Equivalent effect nephograms of meso-scale simulation of triaxial compression at different confining pressures

Fig.14 Load-displacement simulation curves of specimens with different maximum aggregate sizes

Table 7 Comparison of splitting tensile failure modes of specimens with different maximum aggregate sizes

Fig.15 Meso-scale models of concrete with different ITZ characterization methods and layout of penetration

Table 8 Material parameters of concrete components

材料	密度/(kg·m^-3)	泊松比	抗压强度/MPa
骨料	2660	0.2	120
砂浆	2200	0.2	(33, 25, 54)^*
ITZ	1800	0.2	16.5
混凝土	2356	0.2	37

Table 9 Johnson-Cook model parameters of projectile material[43]

材料	A/MPa	B/MPa	n	C
30CrMnSiNi2A	1587	382.5	0.245	0.020

Table 10 Damage simulation results of concrete target with different meso-scale models

试验编号	初速/ (m·s^-1)	DOP/m				H_c/m				D_c/m
试验编号	初速/ (m·s^-1)	试验结果	实体单元法	无ITZ法	粘结失效接触法	试验结果	实体单元法	无ITZ法	粘结失效接触法	试验结果	实体单元法	无ITZ法	粘结失效接触法
S3	1286	0.63	0.64 (1.6%)	0.64 (1.6%)	0.72 (14.3%)	0.19	0.18 (-5.3%)	0.20 (5.3%)	0.22 (15.8%)	0.71	0.64 (-9.9%)	0.62 (-12.7%)	0.62 (-12.7%)
S4	1596	0.78	0.72 (-7.7%)	0.70 (-10.3%)	0.76 (-2.6%)	0.18	0.22 (22.2%)	0.25 (38.9%)	0.25 (38.9%)	0.74	0.72 (-2.7%)	0.70 (-5.4%)	0.67 (-9.5%)
S5	1852	0.64	0.63 (-1.6%)	0.63 (-1.6%)	0.70 (9.4%)	0.25	0.27 (8.0%)	0.30 (20%)	0.30 (20%)	0.81	0.78 (-3.7%)	0.74 (-8.6%)	0.70 (-13.6%)

Fig.16 Target damage nephograms of ITZ solid element method under different penetration velocities

Fig.17 Damage nephograms of meso-scale models during penetration (v0=1852m/s)

Fig.18 Variation of penetration process parameters of different concrete meso-scale models (v0=1852m/s)

Fig.19 Comparison between meso-scale simulated and theoretically calculated results of projectile deceleration

Table 11 Comparison of residual projectile shapes

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