Design and optimization of 3D fast printed cellular structures

This work describes the activity of collaboration between the University of Parma, Department of Engineering and Architecture, and the High Speed 3D Printing Research Center of the National Taiwan University of Science and Technology in Taipei (Taiwan). Several typologies of 3D printed cellular structures are designed with inspiration to the natural world, and printed cells are studied in morphology and mechanical performances, in particular effective density, compressive stiffness, and energy absorption under cyclic loading. Interpretation of experimental testing of printed structures is tried with the support of advanced numerical models. Advantages and limitation of the technique are here shown and discussed. In this brief contribution, three self-supporting lattice structures consististing of repetition of unitary cells are introduced, namely open (structure A), closed thin-walled (structure B) and closed thick-walled cells (structure C), Figure 1. The reticular structures are additively printed using FDM process with TPU filament, and measure sides of 8 mm and thicknesses from 0.8 to 1.2 mm [4]. The structures are designed with a honeycomb criterion, and as all the cellular lattice structures offer advantages in terms of light weight, high resistance to large stresses with great energy absorption [1]. Performances of the structures are experimentally determined by the application of repeated compression cycles with different levels of deformation, respectively 10, 20 and 30% of the specimen height, at the same strain rate. Figure 2 shows some instants of the testing. The stiffness and energy absorption, both percentage and per volume unit, are derived: energy absorption is calculated as the integral of the nominal stress-strain curve, the loss area for the stabilized cycle is evaluated after the application of 20 cyclic loadings and stiffness of the specimen is calculated as the slope of the best fit loading curve. In parallel, a series of FE models are developed within the commercial code ABAQUS© in order to characterize and optimize the 3D printed closed cell structures. The analysis is made starting from a single cell virtually “extracted” from the structure, Figure 1. In this way, given proper boundary conditions to the cell, the mechanical properties, or the study of the deformation behaviour, can be easily and quickly addressed, or several geometrical solutions compared with no need to print and test them all in laboratory. A proper FE model is defined regarding the TPU filament, which behaves as a viscoelastic, hyperelastic material. Also, FDM produces a non-isotropic, layered material structure that is, in most cases, up to twice weaker along the tangential direction than the transversal (Figure 4)[3]. These material properties are incorporated into the FE software through an advanced material model with hyper-elastic and hysteretic capabilities. By the experimental tests, it can be observed that the 30% of compression causes a very large deformation of the lattice structures with barrelling and principle of densification of specimens. As a result, the stiffness always decreases at the deformation increases, both for experimental and numerical tests (Figure 5). Instead, predicted values by the FE analysis are in agreement for the structure A, whilst over-estimate the stiffness of the B and C structures, especially when thick-walled. A and B behave very similarly in term of stiffness and energy absorption, even if with a discrete gap at lower strain levels, while C structure always shows lower performance by about 20%[5]. In this, several factors and their combinations play an important role, including the applied boundary conditions that probably over constrict the transversal dilatation of adjacent cells, the limited strain range of the hysteretic material model which is not sensitive to the other parameters, e.g. the temperature, and the homogenization of the response of a single unit cell, that can drastically limit the deformation. Furthermore, the samples obtained from the FDM process are typically non-uniform at different observation levels and, in general, it is found that numerous process parameters can influence the final mechanical properties of the meld polymer, (presence of pores, building orientation, temperature). In particular, the reticular structures obtained through the FDM process have already proved to be very sensitive also to the combinations of numerous process parameters used in the 3D printing phase[2]. It can be concluded that the combination of all these process parameters, but also material and external conditions, have a great influence on the mechanical properties of the final product. This must be taken into consideration in the design phase, since the results obtained analytically must be suitably analysed in relation to the combined effect of all the possible influencing and acting conditions on the printed part. Regarding the advantages, the study shows that FE analysis can be an effective virtual design tool for studying the behaviour of different lattice structures and for identifying and optimizing their performance, before of running experimental tests.