Page 64 - MSAM-2-1

Materials Science in Additive Manufacturing Energy absorption of Moore’s thin-walled structures

A B

Figure 3. (A) Energy absorbed by the structure represented by the area under force-displacement curve. (B) Energy dissipated by the structure represented
by the area between the loading and unloading force-displacement curve.

caused by cyclic loading, we used an energy dissipation fixed boundary condition was assigned to the bottom
ratio (η), which is defined as the ratio between total reference point.
dissipated energy and total stored energy: Besides, the optimal mesh size was decided after carrying

nd
E out convergence study on the 2 order fractal structure
η = dissipated (VII) (relative density of 20%) loaded from both directions. Mesh
E stored sizes of 0.5 mm, 0.75 mm, 1.5 mm, and 3 mm were applied
for the shell elements. Results of the reaction force versus
2.3. Numerical models and convergence study
displacement curves obtained from simulations are shown
A 3D nonlinear quasi-static finite element (FE) model in Figure 4C and D, corresponding to loading direction 1
was developed to simulate the response of the structures (LD1) and loading direction 2 (LD2), respectively. It could
under compression loading using the commercial be inferred that the mesh size of 0.75 mm is the optimal
software package Abaqus/Explicit 2020 (Dassault Systems considering the model accuracy and computational cost.
SIMULIA Corp., Providence, RI). The material properties Furthermore, a parametric study on 4 order fractal-
th
used in the model were obtained from the tensile tests on inspired thin-walled structures was conducted using FE
3D-printed onyx specimens under ASTM D638, rendering simulations. Limited by Markforged printer’s resolution,
a Young’s modulus value of 1,800 MPa and a yield stress 4 order structures with relative densities of 20%, 30%,
th
of 61 MPa. Adopted from the onyx datasheet provided by and 40% could not be manufactured. Using the FE model,
Markforged, the density and Poisson’s ratio were 1.2 g/cm the energy absorption of higher-order fractal-inspired
3
and 0.3, respectively.
structures was studied.
To reduce the computational cost and maintain large-
scale simulation, the model was simplified by using shell 3. Results and discussion
elements considering a constant wall thickness. The linear 3.1. Effective stress-strain curves
four-node shell elements (S4R) were used to simulate
the fractal structures. Considering that the metallic 3.1.1. Quasi-static compression test results
compression plates of Instron’s universal testing machine The quasi-static compression test of the 2 order fractal
nd
were much stiffer than the 3D-printed Onyx samples, sample is illustrated in Figure 5D. The responses of
two rigid plates were modeled for simplification. The the metamaterials under quasi-static compressive load
shell elements were defined to have a normal contact from in-plane direction 1 are shown in Figure 5A-C,
behavior using hard contact formulation, while a friction corresponding to three different relative densities (20%,
coefficient of 0.3 was utilized to describe the tangential 30%, and 40%, respectively). Curves were constructed
[47]
responses. Two reference points were created, with rigid using the mean effective stress value from three testing
body constraints applied between them and the rigid results. Overall, all the structures underwent large strains
plates. By controlling the boundary conditions on the two with very low stress. Excellent compliance was observed
reference points, the uniaxial compression test conditions up to around 50% strain. As suggested in Figure 5A-C, the
were simulated (Figure 4). A displacement of 35 mm was 3 order thin-walled structures with a relative density of
rd
applied at the top reference point, while an all-direction 20% yielded the most compliant behavior.

Volume 2 Issue 1 (2023) 5 https://doi.org/10.36922/msam.53