A Dynamic Coupled Elastoplastic Damage Model for Rock-like Materials Considering Tension-Compression Damage and Pressure-Dependent Behavior
Abstract
:1. Introduction
2. Establishment of Constitutive Model
2.1. Yield Criterion
2.2. Strain Rate Effect
2.3. Plastic Flow
2.4. Damage Evolution
2.5. Equation of State
- (1)
- The linear elastic zone
- (2)
- The transition zone
- (3)
- The completely dense zone
3. Numerical Implementation of Constitutive Model
4. Determination of Model Parameters
5. Validation of Model
5.1. Example 1: Rock Uniaxial Compression Test
5.2. Example 2: Rock Triaxial Compression Test
5.3. Example 3: Rock Uniaxial Tensile Test
5.4. Example 4: Rock SHPB Test
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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E (GPa) | ρ0 (kg/m3) | ν | c (MPa) | φ | β0 | βm |
---|---|---|---|---|---|---|
24 | 2300 | 0.23 | 21.1 | 25 | 0.8 | 1.037 |
b1 | D1 | D2 | K1 (GPa) | K2 (GPa) | K3 (GP) | μcrush |
1.752 × 10−4 | 0.04 | 1.0 | 96.43 | −813.33 | 4652.09 | 1.197 × 10−3 |
Pcrush (MPa) | μlock | Plock (GPa) | α | |||
17.73 | 0.148 | 2.14 | 50 |
E (GPa) | ρ0 (kg/m3) | ν | c (MPa) | angle φ | β0 | βm |
---|---|---|---|---|---|---|
45.51 | 2720 | 0.32 | 20.56 | 50 | 0.78 | 1.105 |
b1 | μcrush | Pcrush (MPa) | D1 (GPa) | |||
2.64 × 10−3 | 0.633 × 10−3 | 26.67 | 0.05 |
E (GPa) | ρ0 (kg/m3) | ν | σt (MPa) | σc (MPa) | β0 | βm |
---|---|---|---|---|---|---|
58.7 | 1920 | 0.23 | 2.7 | 33 | 1.0 | 1.0 |
b1 | D1 | D2 | K1 (GPa) | K2 (GPa) | K3 (GPa) | μcrush |
0.0 | 0.04 | 1.0 | 9.76 | −21.80 | 401.85 | 3.04 × 10−3 |
Pcrush (MPa) | μlock | Plock (GPa) | α | |||
11.0 | 0.245 | 0.54 | 180 |
Materials | E (GPa) | ν | Ρ0 (kg/m3) | κ (MPa) |
---|---|---|---|---|
VM350 steel | 200 | 0.23 | 8100 | 2500 |
C11000 copper | 117 | 0.35 | 8930 | 750 |
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Hu, X.; Zhang, M.; Xu, W.; Tu, M.; Yin, Z.; Zhang, X. A Dynamic Coupled Elastoplastic Damage Model for Rock-like Materials Considering Tension-Compression Damage and Pressure-Dependent Behavior. Minerals 2022, 12, 851. https://doi.org/10.3390/min12070851
Hu X, Zhang M, Xu W, Tu M, Yin Z, Zhang X. A Dynamic Coupled Elastoplastic Damage Model for Rock-like Materials Considering Tension-Compression Damage and Pressure-Dependent Behavior. Minerals. 2022; 12(7):851. https://doi.org/10.3390/min12070851
Chicago/Turabian StyleHu, Xuelong, Ming Zhang, Wenyao Xu, Min Tu, Zhiqiang Yin, and Xiangyang Zhang. 2022. "A Dynamic Coupled Elastoplastic Damage Model for Rock-like Materials Considering Tension-Compression Damage and Pressure-Dependent Behavior" Minerals 12, no. 7: 851. https://doi.org/10.3390/min12070851
APA StyleHu, X., Zhang, M., Xu, W., Tu, M., Yin, Z., & Zhang, X. (2022). A Dynamic Coupled Elastoplastic Damage Model for Rock-like Materials Considering Tension-Compression Damage and Pressure-Dependent Behavior. Minerals, 12(7), 851. https://doi.org/10.3390/min12070851