PSI - Issue 28

Fuzuli Ağrı Akçay et al. / Procedia Structural Integrity 28 (2020) 1399– 1406 Author name / Structural Integrity Procedia 00 (2019) 000–000

1404

6

corresponds to two unit cells along each three directions, triple lattice corresponds to three unit cells along each three directions, and so forth and so on. Analytical solution is validated through finite element simulations. Two simulations are performed with two different beam lengths. Beam lengths are chosen as � �.8�� mm and � �.7�2 mm, and named as half-length single lattice model and full-length single lattice model, respectively. Those lengths are chosen to be consistent with ID #3 of cubic vertex centroid configuration which has a beam length of � �.7�2 mm and whose cell size in each direction is � � 2 mm. Analytical and finite element results of half-length single lattice model and full-length single lattice model presented in Table 4. The analytical solution for half-length single lattice model represents the analytical strength of cubic vertex centroid lattice with ID #3 as well. Collapse load in numerical simulation corresponds to maximum force experienced during the simulation. Table 4 demonstrates that the difference between analytical and finite element results decreases as the beam length increases. This is an expected outcome as the analytical model is based on a beam model. In other words, analytical model would provide more accurate and reliable results when beam length is much larger compared to cross-section diameter.

Collapse load, F � ( N )

Table 4. Analytical and numerical results of cubic vertex centroid configuration with ID #3.

Beam length, ( mm )

Name

Difference

Analytical

Numerical

Half-length Full-length

0.866 1.732

27.76 13.88

28.30 14.00

1.9% 0.9%

Finite element simulations for double lattice, triple lattice, quadruple lattice, quintuple lattice, and decuple lattice models are performed as well. The results of these simulations are presented in Table 5 along with the experimental result. The table shows that plateau is reached around quadruple lattice model, which consists of four unit cells in each direction.

Table 5. Summary of 2D numerical results. Force ( N ) Numerical

Strength ( MPa ) Numerical Experimental

Single lattice Double lattice Triple lattice

14.0

3.50 6.29 6.78 6.99 7.10 7.28

– – – – –

100.7 244.2 447.1 707.7

Quadruple lattice Quintuple lattice Decuple lattice

2912.1 35.525 Decuple lattice model corresponds to ID #3 of cubic vertex centroid configuration and the corresponding finite element model is presented in Figure 3. The numerical strength for decuple lattice model is obtained as 7.28 MPa whereas the experimental strength of decuple lattice model is obtained as L MPa. The huge difference between these two results suggests that 2D finite element models may not provide accurate results; hence, 3D models need to be utilized for more accurate and reliable results. On the other hand, 2D finite element model captures the shear bands, which is displayed in Figure 4 (a), which is similar to the shear fracture captured in real tests, see Figure 4(b).