Optimal design of cellular structures under random fields

Attenuation or enhancement—a one-dimensional analysis on shock transmission in the solid phase of a cellular material

Planar cellular materials, or honeycombs, are considered as two-phase materials where the properties of one of it phases (voids) degenerates to zero. They are characterized by a low relative density and herein we assume that the solid phase of the material can be modeled as an assembly of axially loaded rods or general flexural elements in infinite and repetitive truss or frame structures, respectively. For the analysis and evaluation of the effective mechanical properties of a 2D cellular material the repetitive structure representing the material is assumed to be in a repetitive stress state. This allows for the analysis to be performed on a single repetitive cell under appropriate boundary conditions. However, all published results refer to cellular materials with repetitive modules possessing at least two orthogonal axes of symmetry. It seems that no general method of analysis of cellular material construed as infinite repetitive structures under periodic stresses for arbitrary repetitive cells is available, unless, as said, the repetitive cell possesses at least two perpendicular axes of symmetry. This is the subject matter of this study - to present a general exact technique to analyze infinite repetitive structures, with nonsymmetrical repetitive cells, under periodic stresses.

The paper gives an overview of issues relating to the characterisation of the progressive collapse of core cellular materials used in sandwich construction. The specific structural application addressed is foreign object impact, and in this case the core cellular material is subject to multi axial stresses, progressive collapse and possible rupture. Crushable foams have been used for many years as core materials. Possible foam materials are based on polymers (e.g. Divinycell, Rohacell), metals (e.g. Alporas) and graphite. It has been shown that the mechanical properties of cellular materials, e.g. elastic behaviour, uniaxial crush and densification, are dependent on the cell geometry, on the cell size (foam density) and on the parent material.

A cellular material was proposed as an ideal candidate for multifunctional material achieving various optimal properties in many length scales. The superior performances on mechanical, thermal, electrical, and fluidic properties have been explored in analytic, numerical, and experimental studies. Since the cellular materials have wide range of potential applications in microscopic devices, characterization in small length scale gains more attentions recently. For this assessment, the atomistic approach as well as continuum approach becomes crucial to characterize its performance in multiscales. One of the key multifunctional features of the nanoporous microstructures would be high fluidic performance. Some studies investigated macroscopic transport properties, but less has been done to address the scale- and shape-dependent transport properties for their microscopic fluidics applications. In this study, we investigated complex flow patterns and transport properties of porous structures in microscopic scales. To address the geometry-dependent transport properties, a non-equilibrium molecular dynamics was employed in the atomistic scale. Various flow channels in the porous materials were introduced to address the size and shape effect of the flow patterns in small length scales.

The correct analysis of shocks in a cellular material

Dynamic stress–strain states for metal foams using a 3D cellular model

Due to the excellent specific energy absorption and high specific strength, cellular materials are widely used in impact protection fields. Higher energy absorption efficiency has always been pursued through designing various structures. According to the bio-inspired design from the growth of ticks and bamboo, this study proposes an easy-to-operate elongation-shortening strategy to improve the mechanical properties of Schwarz Primitive (P) and Schoen Gyroid (G) cells. After that, a gradient design is achieved by combining unit cells with different mechanical properties. The mechanical properties, deformation modes, deformation mechanisms and cyclic response behaviours of the proposed novel cellular materials are investigated by conducting compression testing and finite element analysis. The results show that the elongation-shortening strategy effectively adjusts the configuration of the unit cell, thereby altering the deformation model and optimising energy storage and energy dissipation. Specifically, tensile unit cells exhibit superior energy storage capability. The impact of the elongation-shortening ratio on energy absorption varies across different relative densities. Gradient structures with various elongation-shortening ratios facilitate steady and gradual energy absorption, akin to density-gradient structures. This approach enhances performance by altering the deformation mechanism and expands design possibilities for controlling energy absorption, providing a promising new direction for cellular material design.

Due to their excellent properties, including low weight, high stiffness and strength and heat insulation, cellular materials are widely used in engineering applications, especially in the aerospace and defense industries, as energy absorption devices. To improve the performance of the cellular material, optimization of the material property has attracted considerable research interest. The present research aims to investigate the influence of the gradient on the behavior of graded cellular material under impact conditions. This research program has four parts.

Influence of micro-scale uncertainties on the reliability of fibre-matrix composites

Cellular materials and designed porous materials are a class of materials with extremely low densities and an outstanding combination of mechanical, electrical, thermal, and acoustic properties, based on nature’s way of decreasing the weight of materials such as bone or cork by incorporating cells or pores. These materials are increasingly being considered as lightweight construction, heat exchangers, passive safety and other purposes. Especially, their extraordinary property combinations make them interesting for applications where more than one function is required e.g. high stiffness and fire resistance or acoustic damping. Cellular (or porous) materials are defined as solids containing cells (or pores). They can be classified by morphology and dimensionality as well as formation mechanism, namely; by building up single cells (hollow spheres) or by incorporating cells into bulk material (foam materials). Both approaches lead to three-dimensional cellular materials but with different macroscopic properties, which are determined more by the cell formation mechanism. It is regarded that cellular materials produced by building up hollow spheres give predictable macroscopic properties, compared with those by foaming processes. 1–5) To date, hollow metallic spheres have been produced usually via the coaxial nozzle process using oxide slurry. 6, 7) Compared with the conventional coaxial nozzle process, this paper demonstrates the feasibility of investment process in producing hollow spheres from copper alloys. Optimum processing variables such as slurry viscosity and the mass ratio, hardness, and electrical conductivity of copper hollow spheres with respect to oxide reduction temperature and ZnO content are discussed. 2. Experimental Procedures

Contamination of various food samples became one of the critical issues in food pathogen infection. Food pathogen can be detected by using digital polymerase chain reaction (PCR) and sequencing. These methods were reliable but consuming and take a longer time for detection. The present work describes the innovation to develop a technology to extract double-stranded deoxyribonucleic acid (dsDNA) from food samples and then denatured dsDNA into and single-strand DNA (ssDNA) for further use on the chip using microfluidic device. Microfluidic device is a lab-on-chip device that consist of microfluidic channels that provide paths for biomolecules to flow to individual point of care. DNA extraction is the process by which DNA is separated from proteins, membranes, and other cellular material contained in the cell from which it is recovered. Lysis solution is used in the process of extraction the DNA to break up the cells containing DNA from protein and other cellular materials. This extraction firstly be done in the most labour-intensive in obtaining the DNA biomolecules. Extraction methods may require an overnight incubation, may be a protocol that can be completed in minutes or a couple of hours by using a commercial kit. The disadvantages of the laboratory and commercial kit is due to time-consuming, poor cost-effectiveness, the need to use big laboratory and a complicated process which need an expertise to conduct the experiment and interpret the data. This research is proposed to design and fabricate a microfluidic device that has DNA extraction capabilities. In this research DNA extraction using a commercial kit will be used as a comparison for the quality of the result. The microfluidic device can be used in health care delivery system and will help the doctors in diagnostic process to identify disease of a patient rapidly. Other than that, the output extracted from microfluidic device will be used for DNA probe target interaction for diagnostic kit. The major advantage of microfluidic device is that it consumes less time compared to the conventional chemical methods.

The study of advanced materials aimed at improving human life has been performed since time immemorial. Such studies have created everlasting and greatly revered monuments and have helped revolutionize transportation by ushering the age of lighter–than–air flying machines. Hence a study of the mechanical behavior of advanced materials can pave way for their use for mankind’s benefit. In this school of thought, the aim of this dissertation is to broadly perform two investigations. First, an efficient modeling approach is established to predict the elastic response of cellular materials with distributions of cell geometries. Cellular materials find important applications in structural engineering. The approach does not require complex and time-consuming computational techniques usually associated with modeling such materials. Unlike most current analytical techniques, the modeling approach directly accounts for the cellular material microstructure. The approach combines micropolar elasticity theory and elastic mixture theory to predict the elastic response of cellular materials. The modeling approach is applied to the two dimensional balsa wood material. Predicted properties are in good agreement with experimentally determined properties, which emphasizes the model’s potential to predict the elastic response of other cellular solids, such as open cell and closed cell foams. The second topic concerns intraneural ganglion cysts which are a set of medical conditions that result in denervation of the muscles innervated by the cystic nerve leading to pain and loss of function. Current treatment approaches only temporarily alleviate pain and denervation which, however, does not prevent cyst recurrence. Hence, a mechanistic understanding of the pathogenesis of intraneural ganglion cysts can help clinicians understand them better and therefore devise more effective treatment options. In this study, an analysis methodology using finite element analysis is established to investigate the pathogenesis of intraneural ganglion cysts. Using this methodology, the propagation of these cysts is analyzed in their most common site of occurrence in the human body i.e. the common peroneal nerve. Results obtained using finite element analysis show good correlation with clinical imaging patterns thereby validating the promise of the method to study cyst pathogenesis.

In the Part I of this study, namely the analytical part in Mazor et al. (1992), the governing equations of the phenomenon in which a planar shock wave collides head-on with a cellular material and interacts with it were developed using a Lagrangian approach. In addition, the numerical approach adopted by us during the numerical course of this study was briefly outlined there. The present part reports on experimental and numerical results of the head-on reflection of a planar shock wave with an open cell polyurethane foam. Foams as mentioned by Gibson and Ashby (1988) and summerized in Part I of this study by Mazor et al. (1992), are one of the two general types of cellular materials.

Design rules for modern cable suspension bridges are developed using reliability theories inside a general risk management based framework. In this context, optimal structural design must be considered under the presence of uncertainties in loading, geometry and material properties, whereas the deterministic approaches of optimization neglect the effects of uncertainties associated with design variables. This paper is based on the theory of finite element reliability analysis of geometrically nonlinear elastic structures. It provides computer implementation considerations and developments. For the assessment of overall reliability of suspension bridges, in this paper only static load effects are examined. The sensitivity of the reliability judgments with respect to different loading combinations is also studied.

Here we present the results for fabrication of 3D complex shapes of cellular carbonaceous materials using origami. Cellular carbonaceous materials, particularly carbon and carbide, possess interesting properties including low density, high surface area, high chemical inertness, high oxidation resistance, adjustable electrical conductivity, and high mechanical properties. Due to such properties, they find their use in different applications such as high temperature filters, catalytic support, thermal insulators and structural materials [1,2]. The current state-of-the-art to manufacture cellular carbonaceous materials includes direct foaming method and template method. However, 3D complex shapes, especially with thin cross-sections, are challenging to fabricate in these current techniques. Here we postulate origami-inspired manufacturing to fabricate 3D complex shapes of carbonaceous material. These complex shapes are good candidate for multifunctional materials, as the origami-inspired manufacturing integrates the structural properties of the origami structures to the intrinsic properties of the materials. Furthermore, the potential for scalable manufacturing makes this origami-inspired manufacturing suitable for industry-level production. Our initial target was to fabricate origami structures of glassy carbon and tungsten carbide (WC). Although theoretically numerous shapes can be possible to fabricate, we demonstrated our process using a traditional Miura-ori shape. Here we used Fisherbrand pure cellulose chromatography paper (Sigma Aldrich, Cat. No. 05-714-1) because of its cellulosic nature and minimal impurity. For automatic pre-creasing, we generated CAD models to define the location of the creases. CAD models for the creases on both sides of the paper must be created separately. The chromatography paper was pre-creased using an empty ball-point pen mounted on a cutting plotter machine (Graphtec CE6000-40, USA) using specific equipment parameters. The creasing on the both sides of the paper were automatically aligned by the registration marks generated by the cutting-plotter software and printed on the paper. Figure 1a illustrates an example of a pre-creased paper. Once the pre-creasing was done, the paper was folded manually along the creases to obtain paper origami structures (Figure 1b). The paper origami structure was carbonized at 900 °C for 75 minutes with a heating rate of 5 °C/min in nitrogen environment to obtain origami structures of glassy carbon (Figure 1c). For WC, the paper origami structure was infiltrated with aqueous solution of 20 wt% ammonium metatungstate (AMT). The AMT infiltrated origami shapes were heat-treated at 1300 °C for 3 hours with a heating rate of 2.5 °C/min in vacuum environment to obtain WC origami shape (Figure 1f). In both the cases, the Miura-ori pattern was preserved, although a significant shrinkage occurred during the heat treatment. The heat-treated samples were characterized by x-ray diffraction (XRD) spectroscopy to determine the composition of the material. Scanning electron microscopy (SEM) was used to characterize the microstructures of the precursor paper, carbon and WC origami shapes. The XRD pattern of the carbonized paper (Figure 1d) show weak and broad peaks centered around 2θ = 24° and 2θ = 43°, which corresponds to (022) and (100) reflections of amorphous carbon. Carbonization of the cellulosic paper results in a porous fibril network of glassy carbon as seen in Figure 1e. The fibers feature an average diameter of 5.26 ± 2.53 µm. The pore size distribution among the fibers are random leading to macroporosity with pore diameter ranging from 1.56 µm to 21.71 µm. The results from the XRD of the heat-treated AMT infiltrated paper (Figure 1g) shows the formation of WC, along with a small amount of W2C. The average diameter of fibers forming the fibril matrix of WC is 10.88 ± 2.05 µm (Figure 1h) and the macro-pores caused by the random distribution of the fibers range from 1.04 µm to 28.34 µm. Ongoing work is 1) optimization of WC synthesis process by implementing Taguchi design of experiment; 2) characterization of the mechanical properties of carbon and WC origami shapes; 3) understanding the effect of the microstructures on the mechanical properties of the origami shapes; and 4) use paper a scaffold obtain 3D complex shapes of different other materials such metal impregnated carbon or oxides.