Reza Hedayati

Mechanics of additively manufactured porous biomaterials based on the rhombicuboctahedron unit cell

Thanks to recent developments in additive manufacturing techniques, it is now possible to fabricate porous biomaterials with arbitrarily complex micro-architectures. Micro-architectures of such biomaterials determine their physical and biological properties, meaning that one could potentially improve the performance of such biomaterials through rational design of micro-architecture. The relationship between the micro-architecture of porous biomaterials and their physical and biological properties has therefore received increasing attention recently. In this paper, we studied the mechanical properties of porous biomaterials made from a relatively unexplored unit cell, namely rhombicuboctahedron. We derived analytical relationships that relate the micro-architecture of such porous biomaterials, i.e. the dimensions of the rhombicuboctahedron unit cell, to their elastic modulus, Poissons ratio, and yield stress. Finite element models were also developed to validate the analytical solutions. Analytical and numerical results were compared with experimental data from one of our recent studies. It was found that analytical solutions and numerical results show a very good agreement particularly for smaller values of apparent density. The elastic moduli predicted by analytical and numerical models were in very good agreement with experimental observations too. While in excellent agreement with each other, analytical and numerical models somewhat over-predicted the yield stress of the porous structures as compared to experimental data. As the ratio of the vertical struts to the inclined struts, α, approaches zero and infinity, the rhombicuboctahedron unit cell respectively approaches the octahedron (or truncated cube) and cube unit cells. For those limits, the analytical solutions presented here were found to approach the analytic solutions obtained for the octahedron, truncated cube, and cube unit cells, meaning that the presented solutions are generalizations of the analytical solutions obtained for several other types of porous biomaterials.

Mechanical properties of regular porous biomaterials made from truncated cube repeating unit cells: Analytical solutions and computational models

Additive manufacturing (AM) has enabled fabrication of open-cell porous biomaterials based on repeating unit cells. The micro-architecture of the porous biomaterials and, thus, their physical properties could then be precisely controlled. Due to their many favorable properties, porous biomaterials manufactured using AM are considered as promising candidates for bone substitution as well as for several other applications in orthopedic surgery. The mechanical properties of such porous structures including static and fatigue properties are shown to be strongly dependent on the type of the repeating unit cell based on which the porous biomaterial is built. In this paper, we study the mechanical properties of porous biomaterials made from a relatively new unit cell, namely truncated cube. We present analytical solutions that relate the dimensions of the repeating unit cell to the elastic modulus, Poissons ratio, yield stress, and buckling load of those porous structures. We also performed finite element modeling to predict the mechanical properties of the porous structures. The analytical solution and computational results were found to be in agreement with each other. The mechanical properties estimated using both the analytical and computational techniques were somewhat higher than the experimental data reported in one of our recent studies on selective laser melted Ti-6Al-4V porous biomaterials. In addition to porosity, the elastic modulus and Poissons ratio of the porous structures were found to be strongly dependent on the ratio of the length of the inclined struts to that of the uninclined (i.e. vertical or horizontal) struts, α, in the truncated cube unit cell. The geometry of the truncated cube unit cell approaches the octahedral and cube unit cells when α respectively approaches zero and infinity. Consistent with those geometrical observations, the analytical solutions presented in this study approached those of the octahedral and cube unit cells when α approached respectively 0 and infinity.

Programming the shape-shifting of flat soft matter: from self-rolling/self-twisting materials to self-folding origami

Nature uses various activation mechanisms to program complex transformations in the shape and functionality of living organisms. Inspired by such natural events, we aimed to develop initially flat (i.e. two-dimensional) programmable materials that, when triggered by a stimulus such as temperature, could self-transform their shape into a complex three-dimensional geometry. A two-dimensional starting point enables full access to the surface, e.g. for (nano-)patterning purposes, which is not available in most other manufacturing techniques including additive manufacturing techniques and molding. We used different arrangements of bi- and multi-layers of a shape memory polymer (SMP) and hyperelastic polymers to program four basic modes of shape-shifting including self-rolling, self-twisting (self-helixing), combined self-rolling and self-wrinkling, and wave-like strips. The effects of various programming variables such as the thermomechanical properties of the hyperelastic layer, dimensions of the bi- and multi-layer strips, and activation temperature on the morphology of the resulting three-dimensional objects were studied experimentally and were found to cause as much as 10-fold change in the relevant dimensions. Some of the above-mentioned modes of shape-shifting were then integrated into other two-dimensional constructs to obtain self-twisting DNA-inspired structures, programmed pattern development in cellular solids, self-folding origami, and self-organizing fibers. Furthermore, the possibility of incorporating multiple surface patterns into one single piece of shape-transforming material is demonstrated using ultraviolet-cured photopolymers.

Analytical relationships for prediction of the mechanical properties of additively manufactured porous biomaterials.

Abstract Recent developments in additive manufacturing techniques have motivated an increasing number of researchers to study regular porous biomaterials that are based on repeating unit cells. The physical and mechanical properties of such porous biomaterials have therefore received increasing attention during recent years. One of the areas that have revived is analytical study of the mechanical behavior of regular porous biomaterials with the aim of deriving analytical relationships that could predict the relative density and mechanical properties of porous biomaterials, given the design and dimensions of their repeating unit cells. In this article, we review the analytical relationships that have been presented in the literature for predicting the relative density, elastic modulus, Poissons ratio, yield stress, and buckling limit of regular porous structures based on various types of unit cells. The reviewed analytical relationships are used to compare the mechanical properties of porous biomaterials based on different types of unit cells. The major areas where the analytical relationships have improved during the recent years are discussed and suggestions are made for future research directions.

Mechanical Properties of Additively Manufactured Thick Honeycombs

Honeycombs resemble the structure of a number of natural and biological materials such as cancellous bone, wood, and cork. Thick honeycomb could be also used for energy absorption applications. Moreover, studying the mechanical behavior of honeycombs under in-plane loading could help understanding the mechanical behavior of more complex 3D tessellated structures such as porous biomaterials. In this paper, we study the mechanical behavior of thick honeycombs made using additive manufacturing techniques that allow for fabrication of honeycombs with arbitrary and precisely controlled thickness. Thick honeycombs with different wall thicknesses were produced from polylactic acid (PLA) using fused deposition modelling, i.e., an additive manufacturing technique. The samples were mechanically tested in-plane under compression to determine their mechanical properties. We also obtained exact analytical solutions for the stiffness matrix of thick hexagonal honeycombs using both Euler-Bernoulli and Timoshenko beam theories. The stiffness matrix was then used to derive analytical relationships that describe the elastic modulus, yield stress, and Poisson’s ratio of thick honeycombs. Finite element models were also built for computational analysis of the mechanical behavior of thick honeycombs under compression. The mechanical properties obtained using our analytical relationships were compared with experimental observations and computational results as well as with analytical solutions available in the literature. It was found that the analytical solutions presented here are in good agreement with experimental and computational results even for very thick honeycombs, whereas the analytical solutions available in the literature show a large deviation from experimental observation, computational results, and our analytical solutions.

Additively manufactured metallic pentamode meta-materials

Mechanical metamaterials exhibit unusual mechanical properties that originate from their topological design. Pentamode metamaterials are particularly interesting because they could be designed to possess any thermodynamically admissible elasticity tensor. In this study, we additively manufacture the metallic pentamode metamaterials from a biocompatible and mechanically strong titanium alloy (Ti-6Al-4V) using an energy distribution method developed for the powder bed fusion techniques. The mechanical properties of the developed materials were a few orders of magnitude higher than those of the similar topologies fabricated previously from polymers. Moreover, the elastic modulus and yield stress of the presented pentamode metamaterials were decoupled from their relative density, meaning that the metallic meta-biomaterials with independently tailored elastic and mass transport (permeability) properties could be designed for tissue regeneration purposes.

Effect of bird geometry and orientation on bird-target impact analysis using SPH method

In this study, a real mallard anatomy is numerically created from CT images and then analysed by SPH method. The result produced by the real bird is compared to that of the traditional bird models. The effects of considering the cavities, air and different orientations at which a mallard strikes a target are also investigated. In order to study the effect of orientation of bird on bird-strike events, four impact scenarios were considered and simulated: the impact from bottom, head, tail and wing sides. It was found that the impact from the bottom side is the most damaging scenario, while the impact from the wing side is the safest impact scenario. Distribution of peak and stagnation pressures, impulse transferred to the target and pressure profile for each impact scenario have also been discussed and analysed.

Foam-Core Effect on the Integrity of Tailplane Leading Edge During Bird-Strike Event

The objective of this paper is to describe the procedure of optimizing the leading-edge structure of a tailplane in an industrial environment. The paper also investigates the effect of implementing a foam core between aluminum sheets in a tailplane leading-edge structure. Bird strike against two types of leading-edge structures, one with and the other without a foam core, was investigated and then the optimum design for each case was determined. The results indicate that if a foam core is embedded between the aluminum sheets instead of increasing the thicknesses of aluminum sheets, the skin overall weight can be reduced by 32%.

Fatigue performance of additively manufactured meta-biomaterials: The effects of topology and material type

Additive manufacturing (AM) techniques enable fabrication of bone-mimicking meta-biomaterials with unprecedented combinations of topological, mechanical, and mass transport properties. The mechanical performance of AM meta-biomaterials is a direct function of their topological design. It is, however, not clear to what extent the material type is important in determining the fatigue behavior of such biomaterials. We therefore aimed to determine the isolated and modulated effects of topological design and material type on the fatigue response of metallic meta-biomaterials fabricated with selective laser melting. Towards that end, we designed and additively manufactured Co-Cr meta-biomaterials with three types of repeating unit cells and three to four porosities per type of repeating unit cell. The AM meta-biomaterials were then mechanically tested to obtain their normalized S-N curves. The obtained S-N curves of Co-Cr meta-biomaterials were compared to those of meta-biomaterials with same topological designs but made from other materials, i.e. Ti-6Al-4V, tantalum, and pure titanium, available from our previous studies. We found the material type to be far more important than the topological design in determining the normalized fatigue strength of our AM metallic meta-biomaterials. This is the opposite of what we have found for the quasi-static mechanical properties of the same meta-biomaterials. The effects of material type, manufacturing imperfections, and topological design were different in the high and low cycle fatigue regions. That is likely because the cyclic response of meta-biomaterials depends not only on the static and fatigue strengths of the bulk material but also on other factors that may include strut roughness, distribution of the micro-pores created inside the struts during the AM process, and plasticity. STATEMENT OF SIGNIFICANCE Meta-biomaterials are a special class of metamaterials with unusual or unprecedented combinations of mechanical, physical (e.g. mass transport), and biological properties. Topologically complex and additively manufactured meta-biomaterials have been shown to improve bone regeneration and osseointegration. The mechanical properties of such biomaterials are directly related to their topological design and material type. However, previous studies of such biomaterials have largely neglected the effects of material type, instead focusing on topological design. We show here that neglecting the effects of material type is unjustified. We studied the isolated and combined effects of topological design and material type on the normalized S-N curves of metallic bone-mimicking biomaterials and found them to be more strongly dependent on the material type than topological design.

Mechanical properties of additively manufactured octagonal honeycombs

Honeycomb structures have found numerous applications as structural and biomedical materials due to their favourable properties such as low weight, high stiffness, and porosity. Application of additive manufacturing and 3D printing techniques allows for manufacturing of honeycombs with arbitrary shape and wall thickness, opening the way for optimizing the mechanical and physical properties for specific applications. In this study, the mechanical properties of honeycomb structures with a new geometry, called octagonal honeycomb, were investigated using analytical, numerical, and experimental approaches. An additive manufacturing technique, namely fused deposition modelling, was used to fabricate the honeycomb from polylactic acid (PLA). The honeycombs structures were then mechanically tested under compression and the mechanical properties of the structures were determined. In addition, the Euler-Bernoulli and Timoshenko beam theories were used for deriving analytical relationships for elastic modulus, yield stress, Poissons ratio, and buckling stress of this new design of honeycomb structures. Finite element models were also created to analyse the mechanical behaviour of the honeycombs computationally. The analytical solutions obtained using Timoshenko beam theory were close to computational results in terms of elastic modulus, Poissons ratio and yield stress, especially for relative densities smaller than 25%. The analytical solutions based on the Timoshenko analytical solution and the computational results were in good agreement with experimental observations. Finally, the elastic properties of the proposed honeycomb structure were compared to those of other honeycomb structures such as square, triangular, hexagonal, mixed, diamond, and Kagome. The octagonal honeycomb showed yield stress and elastic modulus values very close to those of regular hexagonal honeycombs and lower than the other considered honeycombs.