The effect of cell size on the mechanical behavior of cellular materials

Predicting the Fracture Toughness of Human Cancellous Bone in Fractured Neck of Femur Patients Using Bone Volume and Micro-Architecture

The current protocol used to determine if an individual is osteoporotic relies on assessment of the individual's bone mineral density (BMD), which allows clinicians to judge the condition of a patient with respect to their peers. This, in essence, evaluates a person's fracture risk, because BMD is a good surrogate measure for strength and stiffness. In recent studies, the authors were the first to produce fracture toughness (FT) data from osteoporotic (OP) and osteoarthritic (OA) patients, by using a testing technique which basically analyzes the prerequisite stress conditions for the onset of growth of a major crack through cancellous bone tissue. FT depends mainly on bone quantity (BV/TV, bone volume/tissue volume), but also on bone micro-architecture (mArch), the inner trabecular design of the bone. The working research hypothesis of the present study is that mArch offers added prediction power to BV/TV in determining FT parameters. Consequently, our aim was to investigate the use of predictive models for fracture toughness and also to investigate if there are any significant differences between the models produced from samples loaded across (AC, transverse to) the main trabecular orientation and along (AL, in parallel) the trabeculae. In multilinear regression analysis, we found that the strength of the relationships varied for a crack growing in these two orthogonal directions. Adding mArch variables in the Ac direction helped to increase the R2 to 0.798. However, in the AL direction, adding the mArch parameters did not add any predictive power to using BV/TV alone; BV/TV on its own could produce R2 = 0.730. The present results also imply that the anisotropic layout of the trabeculae makes it more difficult for a major crack to grow transversely across them. Cancellous bone models and remodels itself in a certain way to resist fracture in a specific direction, and thus, we should be mindful that architectural quality as well as bone quantity are needed to understand the resistance to fracture.

Forged to heal: The role of metallic cellular solids in bone tissue engineering

Metallic cellular solids, made of biocompatible alloys like titanium, stainless steel, or cobalt-chromium, have gained attention for their mechanical strength, reliability, and biocompatibility. These three-dimensional structures provide support and aid tissue regeneration in orthopedic implants, cardiovascular stents, and other tissue engineering cellular solids. The design and material chemistry of metallic cellular solids play crucial roles in their performance: factors such as porosity, pore size, and surface roughness influence nutrient transport, cell attachment, and mechanical stability, while their microstructure imparts strength, durability and flexibility. Various techniques, including additive manufacturing and conventional fabrication methods, are utilized for producing metallic biomedical cellular solids, each offering distinct advantages and drawbacks that must be considered for optimal design and manufacturing. The combination of mechanical properties and biocompatibility makes metallic cellular solids superior to their ceramic and polymeric counterparts in most load bearing applications, in particular under cyclic fatigue conditions, and more in general in application that require long term reliability. Although challenges remain, such as reducing the production times and the associated costs or increasing the array of available materials, metallic cellular solids showed excellent long-term reliability, with high survival rates even in long term follow-ups.

A Review on Mechanical Models for Cellular Media: Investigation on Material Characterization and Numerical Simulation

Cellular media materials are used for automobiles, aircrafts, energy-efficient buildings, transportation, and other fields due to their light weight, designability, and good impact resistance. To devise a buffer structure reasonably and avoid resource and economic loss, it is necessary to completely comprehend the constitutive relationship of the buffer structure. This paper introduces the progress on research of the mechanical properties characterization, constitutive equations, and numerical simulation of porous structures. Currently, various methods can be used to construct cellular media mechanical models including simplified phenomenological constitutive models, homogenization algorithm models, single cell models, and multi-cell models. This paper reviews current key mechanical models for cellular media, attempting to track their evolution from their inception to their latest development. These models are categorized in terms of their mechanical modeling methods. This paper focuses on the importance of constitutive relationships and microstructure models in studying mechanical properties and optimizing structural design. The key issues concerning this topic and future directions for research are also discussed.

Correlation Between the Structure and Compressive Property of PMMA Microcellular Foams Fabricated by Supercritical CO2 Foaming Method

In this study, we fabricated poly (methyl methacrylate) (PMMA) microcellular foams featuring tunable cellular structures and porosity, through adjusting the supercritical CO₂ foaming conditions. Experimental testing and finite element model (FEM) simulations were conducted to systematically elucidate the influence of the foaming parameters and structure on compressive properties of the foam. The correlation between the cellular structure and mechanical properties was acquired by separating the effects of the cell size and foam porosity. It was found that cell size reduction contributes to improved mechanical properties, which can be attributed to the dispersion of stress and decreasing stress concentration.

Mechanical properties and failure behavior of unidirectional porous ceramics

We show that the honeycomb out-of-plane model derived by Gibson and Ashby can be applied to describe the compressive behavior of unidirectional porous materials. Ice-templating allowed us to process samples with accurate control over pore volume, size, and morphology. These samples allowed us to evaluate the effect of this microstructural variations on the compressive strength in a porosity range of 45-80%. The maximum strength of 286 MPa was achieved in the least porous ice-templated sample (P(%) = 49.9), with the smallest pore size (3 μm). We found that the out-of-plane model only holds when buckling is the dominant failure mode, as should be expected. Furthermore, we controlled total pore volume by adjusting solids loading and sintering temperature. This strategy allows us to independently control macroporosity and densification of walls, and the compressive strength of ice-templated materials is exclusively dependent on total pore volume.

Large-deformation and high-strength amorphous porous carbon nanospheres

Carbon is one of the most important materials extensively used in industry and our daily life. Crystalline carbon materials such as carbon nanotubes and graphene possess ultrahigh strength and toughness. In contrast, amorphous carbon is known to be very brittle and can sustain little compressive deformation. Inspired by biological shells and honeycomb-like cellular structures in nature, we introduce a class of hybrid structural designs and demonstrate that amorphous porous carbon nanospheres with a thin outer shell can simultaneously achieve high strength and sustain large deformation. The amorphous carbon nanospheres were synthesized via a low-cost, scalable and structure-controllable ultrasonic spray pyrolysis approach using energetic carbon precursors. In situ compression experiments on individual nanospheres show that the amorphous carbon nanospheres with an optimized structure can sustain beyond 50% compressive strain. Both experiments and finite element analyses reveal that the buckling deformation of the outer spherical shell dominates the improvement of strength while the collapse of inner nanoscale pores driven by twisting, rotation, buckling and bending of pore walls contributes to the large deformation.

The effect of wall thickness distribution on mechanical reliability and strength in unidirectional porous ceramics

Macroporous ceramics exhibit an intrinsic strength variability caused by the random distribution of defects in their structure. However, the precise role of microstructural features, other than pore volume, on reliability is still unknown. Here, we analyze the applicability of the Weibull analysis to unidirectional macroporous yttria-stabilized-zirconia (YSZ) prepared by ice-templating. First, we performed crush tests on samples with controlled microstructural features with the loading direction parallel to the porosity. The compressive strength data were fitted using two different fitting techniques, ordinary least squares and Bayesian Markov Chain Monte Carlo, to evaluate whether Weibull statistics are an adequate descriptor of the strength distribution. The statistical descriptors indicated that the strength data are well described by the Weibull statistical approach, for both fitting methods used. Furthermore, we assess the effect of different microstructural features (volume, size, densification of the walls, and morphology) on Weibull modulus and strength. We found that the key microstructural parameter controlling reliability is wall thickness. In contrast, pore volume is the main parameter controlling the strength. The highest Weibull modulus ([Formula: see text]) and mean strength (198.2 MPa) were obtained for the samples with the smallest and narrowest wall thickness distribution (3.1 [Formula: see text]m) and lower pore volume (54.5%).

Formulation and mechanical properties of emulsion-based model polymer foams

We produce cellular material based on the formulation of model emulsions whose drop size and composition may be continuously tuned. The obtained solid foams are characterized by narrow cell and pore size distributions in direct relation with the emulsion structure. The mechanical properties are examined, by varying independently the cell size and the foam density, and compared to theoretical predictions. Surprisingly, at constant density, Young's modulus depends on the cell size. We believe that this observation results from the heterogeneous nature of the solid material constituting the cell walls and propose a mean-field approach that allows describing the experimental data. We discuss the possible origin of the heterogeneity and suggest that the presence of an excess of surfactant close to the interface results in a softer polymer layer near the surface and a harder layer in the bulk.

The effect of processing variables on morphological and mechanical properties of supercritical CO2 foamed scaffolds for tissue engineering

The porous structure of a scaffold determines the ability of bone to regenerate within this environment. In situations where the scaffold is required to provide mechanical function, balance must be achieved between optimizing porosity and maximizing mechanical strength. Supercritical CO(2) foaming can produce open-cell, interconnected structures in a low-temperature, solvent-free process. In this work, we report on foams of varying structural and mechanical properties fabricated from different molecular weights of poly(DL-lactic acid) P(DL)LA (57, 25 and 15 kDa) and by varying the depressurization rate. Rapid depressurization rates produced scaffolds with homogeneous pore distributions and some closed pores. Decreasing the depressurization rate produced scaffolds with wider pore size distributions and larger, more interconnected pores. In compressive testing, scaffolds produced from 57 kDa P(DL)LA exhibited typical stress-strain curves for elastomeric open-cell foams whereas scaffolds fabricated from 25 and 15 kDa P(DL)LA behaved as brittle foams. The structural and mechanical properties of scaffolds produced from 57 kDa P(DL)LA by scCO(2) ensure that these scaffolds are suitable for potential applications in bone tissue engineering.

The properties of foams and lattices

Man and nature both exploit the remarkable properties of cellular solids, by which we mean foams, meshes and microlattices. To the non-scientist, their image is that of soft, compliant, things: cushions, packaging and padding. To the food scientist they are familiar as bread, cake and desserts of the best kind: meringue, mousse and sponge. To those who study nature they are the structural materials of their subject: wood, coral, cancellous bone. And to the engineer they are of vast importance in building lightweight structures, for energy management, for thermal insulation, filtration and much more. When a solid is converted into a material with a foam-like structure, the single-valued properties of the solid are extended. By properties we mean stiffness, strength, thermal conductivity and diffusivity, electrical resistivity and so forth. And the extension is vast-the properties can be changed by a factor of 1000 or more. Perhaps the most important concept in analysing the mechanical behaviour is that of the distinction between a stretch- and a bending-dominated structure. The first is exceptionally stiff and strong for a given mass; the second is compliant and, although not strong, it absorbs energy well when compressed. This paper summarizes a little of the way in which the mechanical properties of cellular solids are analysed and illustrates the range of properties offered by alternative configurations.

The Effect of Cell Size on the Physical Properties of Crosslinked Closed Cell Polyethylene Foams Produced by a High Pressure Nitrogen Solution Process

The thermal conductivity, thermal expansion, mechanical properties at low strain rates and dynamic mechanical properties of a collection of crosslinked closed cell polyethylene foams manufactured by a high pressure nitrogen solution process have been studied as a function of the cell size. The main mechanisms that influence each property and the foam microstructure have been considered to rationalise the results. A theoretical model has been used to examine the thermal conductivity values. The results have shown the extent to which reducing the cell size could improve the insulating capabilities of these materials. The effect of cell size on the mechanical properties at low strain rates is very small, as a consequence the thermal expansion does not depend on cell size. Nevertheless, the structural characteristics are seen to influence dynamic mechanical response at temperatures below 15°C.

Experimental Analysis of Decohesive Phenomenon in Expanded Polystyrene under Bending and Tensile Loading Conditions

In this paper, the decohesive phenomenon of expanded polystyrene (EPS) is analysed using bending and tensile tests. Globally, the typical stress-strain curve is characterised by a wide linear or nonlinear elastic part, the plastic phase being almost neglected. The mechanical properties, such as the elastic modulus E* and the stress threshold σth*, increase with the EPS apparent density ρ*. The empirical equations have been proposed from experimental data fitting curve. The failure strain called εf, corresponding to the point where the final breakage occurs, decreases when the density value increases. Globally, these observations indicate a brittle behaviour of the EPS material under bending and tensile loading. On the other the hand, scanning electron microscopy (SEM) has been used in order to analyse the EPS fracture surfaces. The trans-beads (TB) fracture mode, where the crack grows through the beads, has sometimes been observed for the high diameters beads. But, according to all observations, the inter-beads (IB) mode generally seems to be the major mode of fracture. Therefore, this indicates that the EPS mechanical strength under bending and tensile loading essentially depends on the beads fusion quality.