PSI - Issue 34

Sanne van den Boom et al. / Procedia Structural Integrity 34 (2021) 87–92

89

Sanne van den Boom et al. / Structural Integrity Procedia 00 (2021) 000–000

3

2 , 000

Youngs Modulus 1940 MPa Poisson Ratio 0.37 Yield stress 50 MPa Mass density 1270 kg / m 3

Homogenized RAMP

1 , 500

1 , 000

(a)

500

0

0 20 Young’s modulus (MPa)

40

80 100

60

Infill density (%)

(b)

(c)

Fig. 2: Overview of the material and infill properties. The table in (a) summarizes the material properties used for PET-G based on in-house measurements and technical data sheets. Figure (b) shows RVE for solid regions in 3-D printed PET-G and (c) illustrates the RAMP interpolation of the homogenized infill properties.

they are homogenized at di ff erent infill densities (see Figure 2c) and interpolated for intermediate densities using Rational Approximation of Material Properties (RAMP) (Stolpe and Svanberg, 2001). For simplicity, it was opted to compute isotropic e ff ective material properties for the infill. It is found that RAMP with p = 3 is a good approximation of the e ff ective material properties of the infill. Design A - uniform infill For the analysis of the uniform infill ladder step, the ladder step geometry is divided into two parts; a 1.5 mm thick wall layer (determined by the printing process) and the infill region. For the wall layer, orthotropic material properties as described above are used, and the infill gets the RAMP interpolation material properties for a density of 30%, to ensure su ffi cient strength in normal working conditions. Design B - optimized infill For the infill optimization, we use the same geometric parts as in the simulations of design A - uniform infill , where only the infill part is considered design domain for optimization. An optimization is performed using Tosca, where the objective is to minimize the compliance. A volume constraint of 30% is used to obtain the same total infill mass as in the previous design and a lower bound of 10% is used on the design variables, to ensure infill is present throughout the entire ladder step. To prevent the optimizer from designing a structure that relies on friction, the boundary conditions are slightly changed during the optimization: the nodes that are supported by the slanted surface are also allowed to move in the transverse direction. Furthermore, in the optimization the structure is loaded by a distributed force instead of a prescribed displacement and only linear elasticity is used. Design C - optimized design For the design optimization the parts are modified slightly: the wall layer is mostly removed, and only kept intact in the locations that touch the slanted surface, the top of the ladder step, and around the holes. Furthermore, material is required to remain at full density between the two holes and in the ribbed top surface to provide su ffi cient sti ff ness. These requirements are based on engineering judgment. The rest of the domain is considered design domain during optimization. Here too, a compliance minimization is performed with a volume constraint of 30%. Instead of the RAMP interpolation, in this case SIMP interpolation (the Tosca default for statics) is used with the standard penalization factor p = 3. The same boundary conditions and loading are used as for the infill optimization in design B - optimized infill . Both optimized ladder steps are illustrated in Figure 3. Non-linear analysis The non-linear analyses that are compared to the experiments use the final designs obtained by the procedure described above, and boundary conditions as described in Section 2. The material behavior is modeled as linear elastic - ideal plastic.

4. Specimen production and experiment

All specimens are printed on a AON3D M2 printer with PET-G HD Glass filament (Formfutura, blinded light grey). Printer settings as described in Figure 4a are used. Design A - uniform infill and design C - optimized design are sliced using Simplify3D. Design B - optimized infill is sliced in Slic3r, as this software allowed the use of helper STLs to locally modify the infill density. Infill densities of 80% for the high density regions, and 20% for the low density