PSI - Issue 28

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

1403

5

Table 2. Analytical and experimental results for cubic vertex centroid lattice. ID Experimental strength ( MPa )

Analytical strength ( MPa ) Relative error

#1 #2 #3 #4

15.864 22.688 35.525 51.604

14.2 27.8 27.8 54.2

-10.5% -22.5% -21.7%

5.0%

3.2. Tetrahedral Vertex Centroid (TVC) Configuration Similar to cubic vertex centroid model, tetrahedral vertex centroid model is based on 4-beam model. Hence, the balance between virtual work and the absorbed work (at collapse) in the plastic hinge yields � � � � � �� � �� � (5) Moreover, the collapse load and the strength of tetrahedral cubic vertex centroid lattice are determined as � � ��� � � � ��√� ��� � � (6) � � �√� � � � � � � � � � � � � � � (7) The ratio between the lattice strength and the yield strength for tetrahedral cubic vertex centroid lattice equals to L power of the relative density as well, i.e., � � ⁄ � �� ��� , and this is consistent with the experimental results. Analytical results along with the experimental results are presented in Table 3. Analytical formulation provides reasonable results only except for Sample #24. It is not clear yet what causes this large error considering the fact that experimental and analytical results are in agreement for the other three samples, Sample #21, #22, and #23.

Table 3. Analytical and experimental results for tetrahedral vertex centroid lattice. ID Experimental strength ( MPa )

Analytical strength ( MPa ) Relative error

#21 #22 #23 #24

8.612

7.1

-17.6% 12.1% 37.6% 82.7%

12.405 10.103 14.835

13.9 13.9 27.1

4. Numerical Analysis Finite element simulations are performed using Abaqus/Standard (Simulia) software. Elastic perfectly-plastic material is utilized with a Poisson’s ratio of � � 0�� , Young’s modulus of � � �0 GPa, and yield strength of σ � � 460 MPa. A friction coefficient of 0.1 is used for contact interaction. 4.1. 2D Finite Element Simulations Only cubic vertex centroid configuration with ID #3 is considered in the simulations. 10 elements are attained in each beam and 2-node linear beam elements (B31) are utilized. Multiple finite element models are considered in the numerical investigation, that is, single lattice, double lattice, triple lattice, quadruple lattice, quintuple lattice, and decuple lattice models are utilized. Single lattice corresponds to one unit cell along each three directions, double lattice