3D Surface-to-Surface Contact Algorithm for SPH Method and Its Application to Simulation of Impact Failure of Ceramic Plate
Abstract
:1. Introduction
2. SPH Formulation
3. 3D SPH Surface-to-Surface Contact Algorithm Using Surface Reconstruction
3.1. 3D Surface Reconstruction of SPH Objects
Algorithm 1: Searching of triangular faces on boundaries of remaining tetrahedrons |
Stage 1 Determine remaining tetrahedrons connected to each particle 1.1. Initialize total number of remaining tetrahedrons connected each particle: nTetPar = 0 1.2. While i ≤ nT do 1.3. While j ≤ 4 do 1.4. Get number of particle at the jth vertice of tetrahedron i: k = Tet(i, j) 1.5. Update total number of tetrahedrons connected to particle k: nTetPar(k) = nTetPar(k) + 1 1.6. Record number of tetrahedron connected to particle k: TetPar(k, nTetPar(k)) = i 1.7. j = j + 1 1.8. i = i + 1 Stage 2 Search boundary faces of remaining tetrahedrons 2.1. Initialize total number of boundary faces and internal face flag: nBndFac = 0, IntFacFlag = False 2.2. While i ≤ nT do 2.3. While j ≤ 4 do 2.4. If IntFacFlag(i, j) is True, then the jth face of tetrahedron i is an internal face, go to step 2.17 2.5. Get numbers of the three particles on the jth face of tetrahedron i: p1, p2, p3 2.6. Get the total number of tetrahedrons connected to particle p1: num = nTetPar(p1) 2.7. While k ≤ num do 2.8. Get the number of the kth tetrahedron connected to particle p1: l = TetPar(p1, k) 2.9. If i = l, then skip tetrahedron l, and go to step 2.15 2.10. While m ≤ 4 do 2.11. Get numbers of the three particles on the mth face of tetrahedron l: q1, q2, q3 2.12. Compare p1, p2, p3 with q1, q2, q3. If they coincide, then go to Step 2.13, else go to 2.14 2.13. Set internal face flags: IntFacFlag(i, j) = True, IntFacFlag(l, m) = True; and go to step 2.17 2.14. m = m + 1 2.15. k = k + 1 2.16. Identify the jth face of tetrahedron i as a boundary face and record the face 2.17. j = j + 1 2.18. i = i + 1 * nT is the total number of remaining tetrahedrons; Loop variables are initialized to be 1 just before loops begin. |
3.2. Detection of Contacts
3.3. Enforcement of Contact Conditions
4. Validation and Application
4.1. Validation Example 1: A Block Sliding along a Slope
4.2. Validation Example 2: Impact between Two Elastic-Plastic Blocks
4.3. Application: High-Velocity Impact of Projectile on Ceramic Plate
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value | Parameter | Value | ||
ρ0/(kg/m3) | 17,162 | Parameters in Grüneisen EOS | S0/(m/s) | 4029 | |
Shear modulus/GPa | 124 | S1 | 1.23 | ||
Parameters in Johnson-Cook strength model | a0/MPa | 1200 | S2 | 0 | |
b0/MPa | 141 | S3 | 0 | ||
n0 | 0.12 | γ0 | 1.54 | ||
c0 | 0.016 | Parameters in damage model | d1 | 0 | |
m0 | 1.0 | d2 | 0.33 | ||
ε0/s−1 | 1.0 | d3 | −1.5 | ||
Tmelt/K | 1723 | d4 | 0 | ||
Troom/K | 300 | d5 | 0 | ||
Cv/(J/(kg·K)) | 134 |
Parameter | Value | Parameter | Value | ||
ρ0/(kg/m3) | 3921 | Parameters in strength model | PT/GPa | 0.2 | |
Shear modulus/GPa | 90.16 | ε0/s−1 | 1.0 | ||
Parameters in strength model | a1 | 0.93 | Conversion fraction of elastic energy loss | 1.0 | |
b1 | 0.31 | ||||
n1 | 0.6 | Parameters in EOS | K1/GPa | 130.95 | |
c1 | 0 | K2/GPa | 0 | ||
m1 | 0.6 | K3/GPa | 0 | ||
HEL/GPa | 2.79 | Parameters in damage model | D1 | 0.005 | |
PHEL/GPa | 1.46 | D2 | 1.0 |
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Xiao, Y.; Liu, K. 3D Surface-to-Surface Contact Algorithm for SPH Method and Its Application to Simulation of Impact Failure of Ceramic Plate. Appl. Sci. 2023, 13, 3790. https://doi.org/10.3390/app13063790
Xiao Y, Liu K. 3D Surface-to-Surface Contact Algorithm for SPH Method and Its Application to Simulation of Impact Failure of Ceramic Plate. Applied Sciences. 2023; 13(6):3790. https://doi.org/10.3390/app13063790
Chicago/Turabian StyleXiao, Yihua, and Kun Liu. 2023. "3D Surface-to-Surface Contact Algorithm for SPH Method and Its Application to Simulation of Impact Failure of Ceramic Plate" Applied Sciences 13, no. 6: 3790. https://doi.org/10.3390/app13063790
APA StyleXiao, Y., & Liu, K. (2023). 3D Surface-to-Surface Contact Algorithm for SPH Method and Its Application to Simulation of Impact Failure of Ceramic Plate. Applied Sciences, 13(6), 3790. https://doi.org/10.3390/app13063790