Damages to aircraft fuselages by ice impactors are categorized as barely visible impact damage (BVID). As the application of composite laminates in manufacturing aircraft fuselage is increasing rapidly, studying hail impact on composite laminates seems crucial. Investigation of variation of delamination area and link-up area for different impact scenarios between ice and carbon fibre prepreg composite plates is the main goal of this study. Link-up refers to joining of delaminated areas created by separate impacts at relatively close impact locations. To this aim, multiple impacts at 1 and up to 6 impact locations and with different impactor energies were simulated using SPH formulation, and delamination areas were quantified. The results showed that as the spacing L between two impact locations increases from 0 to 4R (where R denotes the impactor radius), the total delamination area first shows an increase up to a peak point (usually at R<L<2R) after which it shows a large drop, and after L≈2R, the total delamination area level remains almost constant. The large drop is related to disappearance of the link-up phenomenon beyond a certain spacing. Moreover, it was observed that increasing the number of impact locations increases the delamination area almost linearly. As for the impactor energy influence, the results showed that as the impact energy increases, the threshold spacing for link-up increases. Moreover, for the case of impact at two locations and constant total energy level, two impactors with identical energy level lead to higher delamination area as compared to impactors with non-identical energy levels.

@en

A review of experimental evidence from the literature in relation to “impact fatigue”, “multiple impacts”, and “repeated impacts” on FRP composites, along with articles discussing theoretical and numerical simulations, is provided. A new terminology and definition is presented to clear the meanings of these types of loadings. Experimental investigations about the impact fatigue, have been categorized in terms of the impact energy and the number of impacts. Also, many parameters are considered to illuminate their effects during the repeated impacts on FRP laminates. Discussion of the reported results will be presented along with a recommendation for future explorations and research paths to fill in the knowledge gaps.

@en

Study of porous materials, in particular closed-cell foams, has always attracted researchers’ interest due to the advantages these materials offer in applications where low weight, buoyancy, insulation, or energy absorption is of importance. In this study, quasi-static compressive experimental tests are conducted for low-, medium-, and high-density aluminum foams and their mechanical properties are obtained. In addition, two types of lattice structures based on regular repeating unit cells (Kelvin and Weaire–Phelan) are modelled and their suitability for predicting the mechanical behavior of closed-cell foams in quasi-static configuration is evaluated and compared. Due to the irregular structure of cast foams, it is computationally very expensive to reproduce numerical models with similar structural topology. Using tessellation method can be a step forward in investigating various parameters affecting the properties of closed-cell foams. The results indicated that as compared to Kelvin models, the Weaire–Phelan models better mimic the deformation of manufactured specimens. On the contrary, as compared to the Weaire–Phelan models, the mechanical properties obtained from the Kelvin models are in general closer to the experimental results. The study results also showed that as the foam density increases, the densification strain decreases, while all other mechanical properties (elastic modulus, yield stress, plateau stress, and energy absorption capacity) increase.

@en

The aim of present work is to address nonlinear dynamic thermal buckling of shallow spherical functionally graded porous shells subjected to transient thermal loading using the first order shear deformation theory (FSDT). A power-law distribution as well as cosine-type porosity distribution are used to model the variation of constituents through the shell thickness. Thermomechanical properties are assumed to be temperature dependent. Using Crank–Nicolson time marching scheme, an iterative procedure is employed to solve nonlinear transient heat conduction equation. For thermal boundary conditions, the outer surface of shells is kept at a reference temperature, while the inner surface experiences a sudden temperature rise. Geometrical type of nonlinearity in the sense of von-Karman is taken into account. The highly coupled nonlinear governing equations of motion are extracted by constructing the appropriate weak form and also using multi-term Ritz–Chebyshev method. The resulting ODEs are then reduced to a system of nonlinear algebraic equations by employing the well-known Newmark family of time integration schemes. The latter equations are solved by means of Newton–Raphson iteration procedure. Budiansky criterion is used to recognize critical parameters of dynamic instability of shells due to applied thermal shocks. Some comparison studies are conducted in order to verify the accuracy of results of the present work. Moreover, various parametric studies are performed to assess the influence of involved parameters.

@en

Fiber metal laminates (FMLs) provide a reliable approach for achieving lightweight in high-speed aerospace vehicles. However, the weak interfacial properties between metals and composites could significantly affect the deformation and failure modes of FMLs. In this paper, the low-velocity impact responses and damage mechanisms of CF/PEEK-Ti hybrid laminates with nano-interfacial enhancement by multi-walled carbon nanotubes (CNTs) were characterized and analyzed. The post-impact residual tensile strengths (RTS) were investigated experimentally using quasi-static uniaxial tests combined with digital image correlation, and were evaluated theoretically by developing an analytical prediction model that considers the internal thermal stress and dent geometry. Results show that the initial delamination thresholds of force and displacement during impact can be effectively increased via interfacial enhancement of CNT network. By using a 5% decrease in RTS retention rate as a criterion for damage tolerance, a significant strength decrease starts to appear at 3 J for the sandblasted-only laminates, which is improved to 10 J for the laminates with nano-interfacial enhancement. The proposed unified constitutive model can yield an acceptable prediction for RTS and failure strain of the hybrid laminate after impact, providing a guidance for the structural design and engineering applications of FMLs.@en

@en

We study a special class of mechanical metamaterials, namely lattices, based on beams (struts) with nonuniform cross sections, of which pentamode mechanical metamaterials are a special case. Five symmetric beam types including simple cylinder, concave double cone, convex double cone, concave hyperbolic, and convex hyperbolic are considered. Three types of loads including lateral force, axial force, and moment are applied to the free end of cantilever beams with the five aforementioned geometries and their responses are compared in terms of displacement, normal stress variation along the beam length, and shear stress variation along the beam length. Using the displacement diagrams obtained for different strut geometries and loading conditions, semi-analytical relationships are derived for the displacement at the end of cantilever beams. The semi-analytical relationships are then used to calculate the elastic modulus and yield strength of lattice structures based on two types of unit cells, namely diamond and cube. We also build numerical models and perform experiments to benchmark our semi-analytical results. Comparison of the analytical, numerical, and experimental results demonstrate the accuracy of the semi-analytical relationships presented for the mechanical properties of this class of mechanical metamaterials. Moreover, in both the cube- and diamond-based structures, increasing the α value (i.e., the ratio of the largest to the smallest cross-section radius in each strut) at a constant relative density decreases the elastic modulus, yield strength, the initial maximum stress, and the plateau stress.@en

Metal foams are cellular solids that show some unique properties which cannot be found in other natural or human-made materials. While the impact characteristics of closed-cell foams under static and impact loadings appear to be well-studied in the literature, the impact behaviour of open-cell foams is not yet well-understood. In this study, open-cell foams with two different densities are impacted by drop weights with different kinetic energies. The effects of foam density, impactor initial height, and impactor weight on the recorded stress-time, stress-strain, and energy-strain curves are investigated. While the stress-strain curve of closed-cell foams under impact loading usually consists of a single bell, the results of the current study showed that both the stress-time and stress-strain curves of most the samples consist of two consecutive bells. By increasing weight of the impacting weight, the number of bells increases which helps in increasing the impact period and keeping the maximum generated stress low. Compared to closed-cell foams, the open-cell foams can therefore better absorb the energy, as long as the impact energy is relatively small. The relatively low stiffness as well as the presence of large hollow space inside the open-cell foams also makes them favorable for being used as biomedical scaffolds.@en

Additive manufacturing techniques have made it possible to create open-cell porous structures with arbitrary micro-geometrical characteristics. Since a wide range of micro-geometrical features is available for making an implant, having a comprehensive knowledge of the mechanical response of cellular structures is very useful. In this study, finite element simulations have been carried out to investigate the effect of structure unit cell type (cube, rhombic dodecahedron, Kelvin, Weaire-Phelan, and diamond), cross-section type (circular, square, and triangular), strut length, and relative density on the Young's modulus, shear modulus, yield stress, shear yield stress, and Poisson's ratio of open-cell tessellated cellular structures. It was desired to see whether or not and to what extent each of the aforementioned parameters affect the mechanical properties of a porous structure. It was seen that the strut cross-section type does not have a considerable effect on the structure Young's modulus while its effect on the structure yield stress is significant. The strut length was not effective on the mechanical properties if the relative density was kept constant. It was also observed that the structure unit cell type and relative density have a considerable effect on the elastic properties. The highest and the lowest stiffness and strength belonged to the cube and diamond unit cell types, respectively. The rhombic dodecahedron structure with circular cross-section had a high yielding strength (second among all the cases) while its Young's modulus was relatively low. Therefore, it is the best choice for applications with low stiffness requirements, such as biomedical implants.

@en

The response of Glare 3 and Glare 5 to repeated impacts and dropped tools was experimentally investigated using drop weight equipment. Two repetition sequences were tested. The first sequence consisted of successive impacts with the same impact energy, but lower than the first impact. In the second sequence the rebound energy of one impact was taken as the impact energy for the subsequent impact. This sequence represents the drop weight impact. The damage was evaluated using visual inspection and ultrasonic C-scan. Three categories of impact damage were observed: visible deformation without internal or external damage, visible internal damage (C-scan) without external damage, and visible internal and external damages. The “threshold energy” defined as the magnitude of maximum impact energy in successive impacts that caused no further damage after the first impact. For the successive impacts with energy between the threshold energy and the first impact, repeated impacts were observed to cause damage propagation. Successive impacts with impact energy less than the threshold did not reveal any effect on the structural integrity. The dropped tool sequence revealed that the rebound energies do not have a considerable effect; the force–time and force–displacement curves for Glare laminates did not change with successive rebound impacts. Therefore, it can be concluded that damage propagation due to rebound energies is negligible.

@en

Although the initial mechanical properties of additively manufactured porous biomaterials are intensively studied during the last few years, almost no information is available regarding the evolution of the mechanical properties of implant-bone complex as the tissue regeneration progresses. In this paper, we studied the effects of tissue regeneration on the static and fatigue behavior of selective laser melted porous titanium structures with three different porosities (i.e. 77, 81, and 85%). The porous structures were filled with four different polymeric materials with mechanical properties in the range of those observed for de novo bone (0.7 GPa

@en

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. @en

Low-density open-cell porous structures are widely researched due to their mechanical properties that are close to natural bone and their open-cell interconnected structure that allows for ingrowth of new bone tissue. Different studies have shown that apparent density dominates the mechanical properties of porous lattice structures. Surveying the literature revealed that in the previously published studies, there are inaccuracies in calculating the apparent density. In this study, the effects of considering exact apparent density rather than approximate density on the predicted elastic modulus, yield stress, and Poisson's ratio were investigated. The accuracy of the created models was evaluated by comparing their mechanical properties with corresponding experimental data. Five different types of unit cell, namely cube, rhombic dodecahedron, Weaire-Phelan, Kelvin, and diamond and three different cross-section geometries namely circle, square, and triangle were considered. The effects of unit cell type, cross-section type, and apparent density on the elastic moduli of open-cell tessellated cellular structures were also investigated. Considering exact density instead of approximate density increased the calculated elastic modulus and yield stress of structures with different morphologies by 22%-44% for an apparent density of 50%. Inversely, using exact apparent density instead of approximate apparent density decreased the Poisson's ratio values.

@en

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, Poisson's 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, Poisson's 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.

@en

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, Poisson's 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.

@en

The mechanical behavior of additively manufactured porous biomaterials has recently received increasing attention. While there is a relatively large body of data available on the static mechanical properties of such biomaterials, their fatigue behavior is not yet well-understood. That is partly because systematic study of the fatigue behavior of these porous biomaterials is time-consuming and expensive due to the large number of involved factors. In the current study, we propose a computational approach based on finite element method that could be used to predict the fatigue behavior of porous biomaterials given their type of repeating unit cell, dimensions of the unit cell, and S-N curve of the parent material. We applied the proposed approach to predict the fatigue behavior of porous titanium alloy (Ti-6Al-4V) biomaterials manufactured using selective laser melting based on the rhombic dodecahedron unit cell and compared our computational results with experimental observations from one of our recent studies. The evolution of the displacement, elastic modulus, and number of failed struts vs. the number of loading cycle followed a two-stage pattern. In the first stage, there was a relatively slow rate of change in the above-mentioned variables, while they changed very rapidly in the second stage. That compares to the behavior observed in our experimental study. The computationally predicted S-N curve well matched the experimental observations for stress levels not exceeding 60% of the yield stress of the porous structures. For higher stress levels, the presented approach substantially underestimated the fatigue life of the porous structures. The effects of the irregularities caused by the additive manufacturing process on the fatigue behavior of the porous structures were also studied. It was found that those irregularities substantially decrease the fatigue life particularly for lower stress levels.

@en

Today, interconnected open-cell porous structures made of titanium and its alloys are replacing the prevalent solid metals used in bone substitute implants. The advent of additive manufacturing techniques has enabled manufacturing of open-cell structures with arbitrary micro-structural geometry. In this paper, rhombic dodecahedron structures manufactured using SLM technique and tested by Amin Yavari et al. (2014) are investigated numerically using ANSYS and LS-DYNA finite element codes for the modeling of the elastic and postyielding behavior of the lattice structure, respectively. Implementing a micro-mechanical approach to the numerical modeling of the yielding behavior of open-cell porous materials is the main contribution of this work.One of the advantages of micro-mechanical modeling of an open-cell structure is that, in contrast to the macro-mechanical finite element modeling, it is not necessary to obtain several material constants for different foam material models through heavy experimental tests. The results of the study showed that considering the irregularity in defining the cross-sections of the struts decreases both the yielding stress and densification strain of the numerical structure to the values obtained from the experimental tests. Moreover, the stress-strain curve of the irregular structure was much smoother in two points of yielding and densification, which is also observable in experimental plots. Considering the irregularity in the structure also decreased the elastic modulus of the lattice structure by about 20-30%. The post-densification modulus was more influenced by irregularity as it was decreased by more than 50%. In summary, it was demonstrated that using beam elements with variable cross-sections for constructing open-cell biomaterials could result in numerical results sufficiently close to the experimental data.

@en