Controlling auxeticity in curved-beam metamaterials via a deep generative model

Lattice-based mechanical metamaterials are known to exhibit quite a unique mechanical behavior owing to their rational internal architecture. This includes unusual properties such as a negative Poisson's ratio, which can be easily tuned in reentrant-hexagonal metamaterials by adjusting the angles between beams. However, changing the angles also affects the overall dimensions of the unit cell. We show that by replacing traditional straight beams with curved ones, it is possible to control Poisson's ratio of reentrant-hexagonal metamaterials without affecting their overall dimensions. While the mechanical properties of these structures can be predicted through finite element simulations or, in some cases, analytically, many applications require to identify architectures with specific target properties. To solve this inverse problem, we introduce a deep learning framework for generating metamaterials with desired properties. By supplying the generative model with a guide structure in addition to the target properties, we are not only able to generate a large number of alternative architectures with the same properties, but also to express preference for a specific shape. Deep learning predictions together with experimental measurements prove that this approach allows us to accurately generate unit cells fitting specific properties for curved-beam metamaterials

Femur auxetic meta-implants with tuned micromotion distribution

Stress shielding and micromotions are the most significant problems occurring at the bone-implants interface due to a mismatch of their mechanical properties. Mechanical 3D metamate-rials, with their exceptional behaviour and characteristics, can provide an opportunity to solve the mismatch of mechanical properties between the bone and implant. In this study, a new porous femoral hip meta-implant with graded Poisson’s ratio distribution was introduced and its results were compared to three other femoral hip implants (one solid implant, and two porous meta-implants, one with positive and the other with a negative distribution of Poisson’s ratio) in terms of stress and micromotion distributions. For this aim, first, a well-known auxetic 3D re-entrant structure was studied analytically, and precise closed-form analytical relationships for its elastic modulus and Poisson’s ratio were derived. The results of the analytical solution for mechanical properties of the 3D re-entrant structure presented great improvements in comparison to previous analytical studies on the structure. Moreover, the implementation of the re-entrant structure in the hip implant provided very smooth results for stress and strain distributions in the lattice meta-implants and could solve the stress shielding problem which occurred in the solid implant. The lattice meta-implant based on the graded unit cell distribution presented smoother stress-strain distribution in comparison with the other lattice meta-implants. Moreover, the graded lattice meta-implant gave minimum areas of local stress and local strain concentration at the contact region of the implants with the internal bone surfaces. Among all the cases, the graded meta-implant also gave micromotion levels which are the closest to values reported to be desirable for bone growth (40 µm).</p

Improving the accuracy of analytical relationships for mechanical properties of permeable metamaterials

Permeable porous implants must satisfy several physical and biological requirements in order to be promising materials for orthopaedic application: they should have the proper levels of stiffness, permeability, and fatigue resistance approximately matching the corresponding levels in bone tissues. This can be achieved using designer materials, which exhibit exotic properties, commonly known as metamaterials. In recent years, several experimental, numerical, and analytical studies have been carried out on the influence of unit cell micro-architecture on the mechanical and physical properties of metamaterials. Even though experimental and numerical approaches can study and predict the behaviour of different micro-structures effectively, they lack the ease and quickness provided by analytical relationships in predicting the answer. Although it is well known that Timoshenko beam theory is much more accurate in predicting the deformation of a beam (and as a result lattice structures), many of the already-existing relationships in the literature have been derived based on Euler–Bernoulli beam theory. The question that arises here is whether or not there exists a convenient way to convert the already-existing analytical relationships based on Euler–Bernoulli theory to relationships based on Timoshenko beam theory without the need to rewrite all the derivations from the start point. In this paper, this question is addressed and answered, and a handy and easy-to-use approach is presented. This technique is applied to six unit cell types (body-centred cubic (BCC), hexagonal packing, rhombicuboctahedron, diamond, truncated cube, and truncated octahedron) for which Euler–Bernoulli analytical relationships already exist in the literature while Timoshenko theory-based relationships could not be found. The results of this study demonstrated that converting analytical relationships based on Euler–Bernoulli to equivalent Timoshenko ones can decrease the difference between the analytical and numerical values for one order of magnitude, which is a significant improvement in accuracy of the analytical formulas. The methodology presented in this study is not only beneficial for improving the already-existing analytical relationships, but it also facilitates derivation of accurate analytical relationships for other, yet unexplored, unit cell types.</p

Curly beam with programmable bistability

Bistable beams with prebuckled sinusoidal shape are prominently constructed into mechanical metamaterial unit cells with bi- and multi-stability. While the effects of boundary conditions and thickness on their bistability were more studied, few investigations have been focused on the effect of the beam shape. We systematically created new geometries by adding a second sinusoidal term varying in amplitudes and wavelengths, onto the prebuckled bistable beam shape. Nonlinear large deformation finite element modeling showed effective tuning of the forward and backward forces, snapping energy, and the maximum strain, by the wavelength and amplitude. Decent improvements in the overall stability of their second stable state were observed. The enhancement of the relatively weak snap-through behavior of the single beams was demonstrated by pairing a large variety of curly beams into double-beam configurations. Experimental observations on the 3D printed polylactic acid unit cells strongly supported the simulation results, and demonstrated the possibility of building multistable structures. The design of bistable beams with consistent thickness and comparable overall shapes, yet differing mechanical behavior, has opened up new avenues for the development of bi- and multistable structures in programmable mechanical metamaterials, particularly with materials fabricated at the resolution limit of the respective techniques