Effective Compressive Modulus Research Articles

Analytical and Numerical Study of the Axial Stiffness of Fiber-Reinforced Elastomeric Isolators (FREIs) under Combined Axial and Shear Loads

Fiber-reinforced elastomeric isolators (FREIs) are rubber-based seismic devices introduced as a low-cost alternative to steel-reinforced elastomeric isolators (SREIs). They are generally used in unbonded applications, i.e., friction is used to transfer the lateral loads from the upper to the lower structure. Under combined axial and shear loads, the lateral edges of the unbonded bearings detach from the top and bottom supports resulting in a rollover deformation. Due to increasing horizontal displacement, the overlap area of the bearing decreases; thus, the vertical properties of the device are a function of the imposed lateral deformation. This paper introduces a closed-form solution to derive the vertical stiffness of the bearings as a function of the horizontal displacement. The variations of the vertical stiffness and of the effective compressive modulus of square-shaped FREIs are given in this work. The analytical results are then validated through a comparison with the outputs of a parametric finite element analysis of FREIs, including different mechanical and geometric parameters.

A Study on Effective Compressive and Shear Properties of Tetrahedral Lattice Materials

Tetrahedral lattice materials can be used as the core of a sandwich structure. The properties of tetrahedral lattice materials can be controlled by modifying their geometrical parameters and relative density. In this paper, a tetrahedral lattice structure deformation mechanism-based theoretical analysis model is established to predict the effective mechanical properties of the structure under compressive and shear loadings. The analytical solutions are subsequently verified by finite element analysis of a large-scale lattice material model. Based on the obtained results, the effects of the geometrical parameters, relative density, and shear deformation are discussed. At a specific relative density, as strut inclination angle increases: (1) the effective compressive modulus in the z-direction increases; (2) the effective compressive modulus in x- and y-directions, and the effective shear modulus in xy-, xz-, and yz-directions firstly increases but then decreases; (3) the effective Poisson’s ratios [Formula: see text] and [Formula: see text] increase, whereas, [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] decrease. With an increase in relative density, the effective compressive and shearing modulus increase, the effective Poisson’s ratios remain constant, [Formula: see text] and [Formula: see text] are always equal to 0 when the strut inclination angle is [Formula: see text]. The effect of shear deformation on the effective mechanical properties increases as the slenderness ratio increases. The predicted effective properties enable the tetrahedral lattice unit cells to be treated as “material” in the design and analysis process.

Vertical response of unbonded fiber reinforced elastomeric isolators (U-FREIs) under bidirectional shear loading

Fiber Reinforced Elastomeric Isolators (FREIs) were generally studied in unbonded configuration. Due to combined axial and shear loads, the contact area between the bearing and horizontal supports reduces with the horizontal displacement. As a result, both the vertical and the horizontal stiffnesses decrease with the horizontal deformation while also the vertical deformation increases. This paper presents the results of a large set of full-scale 3D Finite Element Analyses on unbonded fiber reinforced bearings with different geometries, subjected to combined axial and multi-directional shear loads. The main vertical response parameters were studied, namely the vertical displacement, the vertical stiffness, and the effective compressive modulus, thus highlighting the influence of both geometry and horizontal loading direction on the vertical response of the FREIs. Conclusion of this study demonstrate to what extent the combined influence of geometric properties and loading conditions affects the vertical response of elastomeric bearings with flexible reinforcements.

Influence of the parameters of the convolutional neural network model in predicting the effective compressive modulus of porous structure.

In recent years, the convolutional neural network (CNN) technique has emerged as an efficient new method for designing porous structure, but a CNN model generally contains a large number of parameters, each of which could influence the predictive ability of the CNN model. Furthermore, there is no consensus on the setting of each parameter in the CNN model. Therefore, the present study aimed to investigate the sensitivity of the parameters in the CNN model for the prediction of the mechanical property of porous structures. 10,500 samples of porous structure were randomly generated, and their effective compressive moduli obtained from finite element analysis were used as the ground truths to construct and train a CNN model. 8,000 of the samples were used to train the CNN model, 2000 samples were used for the cross-validation of the CNN model and the remaining 500 new structures, which did not participate in the CNN training process, were used to test the predictive power of the CNN model. The sensitivity of the number of convolutional layers, the number of convolution kernels, the number of pooling layers, the number of fully connected layers and the optimizer in the CNN model were then investigated. The results showed that the optimizer has the largest influence on the training speed, while the fully connected layer has the least impact on the training speed. Additionally, the pooling layer has the largest impact on the predictive ability while the optimizer has the least impact on the predictive ability. In conclusion, the parameters of the CNN model play an important role in the performance of the CNN model and the parameter sensitivity analysis can help optimize the CNN model to increase the computational efficiency.

Predicting the effective compressive modulus of human cancellous bone using the convolutional neural network method

The efficient prediction of biomechanical properties of bone plays an important role in the assessment of bone quality. However, the present techniques are either of low accuracy or of high complexity for the clinical application. The present study aims to investigate the predictive ability of the evolving convolutional neural network (CNN) technique in predicting the effective compressive modulus of porous bone structures. The T11/T12/L1 segments of thirty-five female cadavers were scanned using the HR-pQCT scanner and the images obtained from it were used to generate 10896 2 D bone samples, in which only the cancellous bony parts were processed and investigated. The corresponding 10896 heterogeneous finite-element (FE) models were generated, and then a CNN model was constructed and trained using the predictions of the FE analysis as the ground truths. Then the remaining 260 bone samples generated from the initial HR-pQCT images were used to test the predictive power of the CNN model. The results show that the coefficient of the determinant (R 2) from the linear correlation between the CNN and FE predicted elastic modulus is 0.95, which is much higher than that from the correlation between the BMD and the FE predictions (R 2 = 0.65). Furthermore, the 95th and 50th percentiles of relative prediction error are below 0.28 and 0.09, respectively. In the conclusion, the CNN model can efficiently predict the effective compressive modulus of human cancellous bone and can be used as a promising and clinically applicable method to evaluate the mechanical quality of porous bone.

An analytical method to calculate effective elastic properties of mapped rhombic dodecahedron structures fabricated with electron beam melting

Cellular rhombic dodecahedron (RD) structures fabricated in Ti6Al4V using the electron beam melting (EBM) process have been proposed for tissue scaffolds and medical implants that approximate the properties of bone. The mechanical properties of these structures have often been determined through compressive tests. The introduction of a uniaxial mapping ratio allows structures with personalized parameters and desired mechanical properties to be manufactured with respect to different border constraints without changing the porosity of the structure. In this study, a non-linear relationship between the effective modulus of elasticity and the number of cells was found for periodically arranged RD porous structures, and there were discrepancies in the modulus for different mapping ratios of specimens having the same size. An analytical model based on beam theory is therefore proposed to estimate the effective compressive elastic modulus and Poisson's ratio for such phenomenon. The analytical model predicts cases including 1 × 1 to ∞ ×∞ cells without boundary constraints and arbitrary m× n with boundary constraints, among which the 1 × 1 and ∞ ×∞ cases without boundary constraints give the lower and upper limits of the effective compressive modulus, respectively. The prediction accuracy of m× n cells with analytical solutions was verified by beam elements neglecting shearing effects in the FE method, and both gave identical results under the same constraints. However, the analytical method has advantages that are difficult to replace when dealing with models where the number and dimension of cells far exceed the computational capacity of numerical simulations. Influenced by surface quality, the effective modulus of the actual test is generally between the values predicted by the input-defined inner and outer diameters of the strut as an input.

Compensating the anisotropic mechanical properties of electron beam melting-based Gyroid scaffolds using structural design

In recent years, scaffolds based on triply periodic minimal surface (TPMS) have been identified as one of the candidates for bone repair materials because of their excellent mechanical and biological properties. In addition, additive manufacturing (AM) enables the production of porous scaffolds with complex microstructures. However, some AM methods (e.g., electron beam melting, EBM) tend to produce a significant anisotropic discrepancy in the mechanical response of scaffolds, and neither the underlying mechanisms nor the compensation method for this discrepancy is clear so far. The aim of this study was to compensate for this discrepancy using structural design and to reveal the underlying mechanisms of each impact factor. Four types of Gyroid scaffolds ranging from rotational symmetric to obvious anisotropic were produced along the height direction of the scaffold using EBM technique, and the relationship between the degree of structural anisotropy (DA) and compressive modulus was determined. When the value of DA was 1.08, the compressive modulus in the building and non-building directions were equal, which means that the anisotropic mechanical discrepancy generated by EBM process was compensated. On the other hand, the decoupling of factors affecting mechanical properties showed that the effective compressive modulus of the rotational symmetric scaffold in the building direction was 42.6% lower than that of non-building direction in the finite element model with highly reductive geometry, while the discrepancy in experimental method was only 20%. The results suggest that the geometric discrepancy is the main factor of the mechanical discrepancy, and the orientation of columnar grains is inclined to the building direction which helps to alleviate the mechanical anisotropy caused by geometry discrepancy. The findings of this study provide important information for the application of TPMS scaffolds in bone implants.

Development and assessment of modified-honeycomb-structure scaffold for bone tissue engineering

Scaffolds for bone tissue engineering should have sufficient mechanical properties comparable with those of the surrounding native bone tissue. Therefore, it is necessary to improve the mechanical properties, especially compressive strength, of 3D scaffolds for bone tissue engineering applications. Various studies have focused on the variation or manipulation of structures or materials, for example, the Kagome-structure scaffold or polycaprolactone/hydroxyapatite composite scaffold. In this study, we propose a modified honeycomb structure for 3D bone-tissue-engineering scaffolds. This is a 3D honeycomb structure with pores at its walls to enhance the interconnectivity. The honeycomb structure is known to be the strongest structure with respect to its weight. Therefore, the honeycomb structure inspired us to apply it to bone-tissue-engineering scaffolds, and its 3D interconnectivity was enhanced by adding pores in its walls without a considerable decrease in its mechanical strength. By means of numerical analysis, the compressive stiffness of the modified-honeycomb-structure scaffold was investigated, and it was found that the effective compressive modulus of the modified-honeycomb-structure scaffold was significantly superior to those of Kagome-structure and grid-structure scaffolds having similar porosity of 50% and main pore size of 500 µm. Meanwhile, the Kagome-structure scaffold had the highest compressive modulus among the reported 3D interconnected scaffolds. Moreover, the modified-honeycomb-structure scaffolds were successfully fabricated with polycaprolactone (PCL) using a lab-made bio-printer with a precision extrusion deposition (PED) system employing a nozzle with a size of 50 µm, and a compressive test using a UTM was performed to prove the numerical result, in which the effective compressive modulus of the modified-honeycomb-structure scaffold was found to be superior to that of the Kagome-structure scaffold. Furthermore, we assessed cell proliferation, and the modified-honeycomb-structured scaffold was more favorable for cell proliferation than the Kagome-structure and grid-structure scaffolds. • Modified-honeycomb scaffold was proposed and successfully fabricated with PCL. • Compressive stiffness of proposed scaffold was evaluated numerically. • Compressive stiffness of proposed scaffold was validated experimentally. • Proposed scaffold has the highest compressive stiffness among the control groups. • Proposed scaffold promote in-vitro cell behavior similar to the control groups.

Machine learning for 3D printed multi-materials tissue-mimicking anatomical models

Polyjet, a material jetting 3D printing technique, has been widely used for the fabrication of patient-specific anatomical models owing to the toolless fabrication technique and its ability to print multiple materials in a single part. Although the fabrication of anatomical models with high dimensional accuracy has been demonstrated, 3D printed anatomical models with tissue-mimicking properties have not been realized. In this study, a composite layering design was used to tune the shore hardness and compressive modulus of the Polyjet-printed parts in an attempt to mimic the properties of human tissues. 216 specimens (with 72 combinations of design parameters) were printed and tested to develop the material library for the anatomical models. An analytical model was developed to estimate the effective compressive modulus and shore hardness of the composite laminate. A neural network was used to learn the multi-dimensional relationship between the design parameters and mechanical properties. The 5-33-2 network size is found to be the optimum neural network structure with a mean square error of 0.98% for the compressive modulus, lower than the traditional response surface method model. A genetic algorithm was used to search the design space for the most optimum design parameters for the targeted effective shore hardness.

Effective compressive elastic behavior of rhombic dodecahedron structure with and without border constraints

The effective compressive elastic modulus of the cellular rhombic dodecahedron structure, with m × n cells in the X- and Y- directions in matrix, has been studied. The effective compressive elastic modulus of the structure without border constraint is a function of m and n; while for the structure with border constraints in the X- and Y- directions it is found unique that is independent of m and n, and is a function of the porosity of the structure. In order to study and understand the range of the effective compressive elastic modulus for the structure without border constraint with explicit expression of the structure parameters, an analytical model has been developed to evaluate the lower and upper bounds. The analytical model is also valid for the structure with double border constraints with a unique modulus. In addition, a finite element method based on beam theory in neglecting shearing effect has been developed for both cases, under the specific boundary conditions used in a unit cell, including finite and infinite numbers of cells m or/and n.As such, the analytical method based on beam theory takes into consideration the finite geometry dimensions and the fictive infinite geometry dimensions. The later gives the upper bound of the effective compressive elastic modulus. The modulus of the structure composed of finite numbers of cells m × n without border constraint is not only a function related to the porosity of the structure, but the geometrical parameters d and b. An experimental test has been fulfilled and compared to the theoretical one with reasonable agreement.

Quantifying the discrepancies in the geometric and mechanical properties of the theoretically designed and additively manufactured scaffolds

In recent years, the triply periodic minimal surface (TPMS) has emerged as a new method for producing open cell porous scaffolds because of the superior properties, such as the high surface-to-volume ratio, the zero curvature, etc. On the other hand, the additive manufacturing (AM) technique has made feasible the design and development of TPMS scaffolds with complex microstructures. However, neither the discrepancy between the theoretically designed and the additively manufactured TPMS scaffolds nor the underlying mechanisms is clear so far. The aims of the present study were to quantify the discrepancies between the theoretically designed and the AM produced TPMS scaffolds and to reveal the underlying mechanisms, e.g., the effect of building orientation on the discrepancy. 24 Gyroid scaffolds were produced along the height and width directions of the scaffold using the selective laser melting (SLM) technique (i.e., 12 scaffolds produced in each direction). The discrepancies in the geometric and mechanical properties of the TPMS scaffolds were quantified. Regarding the geometric properties, the discrepancies in the porosity, the dimension and the three-dimensional (3D) geometry of the scaffolds were quantified. Regarding the mechanical properties, the discrepancies in the effective compressive modulus and the mechanical environment (strain energy density) of the scaffolds were evaluated. It is revealed that the porosity in the AM produced scaffold is approximately 12% lower than the designed value. There are approximately 68.1 ± 8.6% added materials in the AM produced scaffolds and the added materials are mostly distributed in the places opposite to the building orientation. The building orientation has no effect on the discrepancy in the scaffold porosity and no effect on the distribution of the added materials (p > 0.05). Regarding the mechanical properties, the compressive moduli of the scaffolds are 24.4% (produced along the height direction) and 14.6% (produced along the width direction) lower than the designed value and are 49.1% and 43.6% lower than the μFE counterparts, indicating that the imperfect bonding and the partially melted powders have a large contribution to the discrepancy in the compressive modulus of the scaffolds. Compared to the values in the theoretically designed scaffold, the strain energy densities have shifted towards the higher values in the AM produced scaffolds. The findings in the present study provide important information for the design and additive manufacturing of TPMS scaffolds.

Numerical predictions of the interaction between highly nonlinear solitary waves and the microstructure of trabecular bone in the femoral head

The unique properties of highly nonlinear solitary waves in granular chains have prompted extensive research in the area of non-destructive testing and led to the development of new diagnostic schemes with potential applications in the healthcare industry. Here, we study numerically the interaction between highly nonlinear solitary waves in a granular chain and the microstructure of trabecular bone in the femoral head. High-resolution finite element models of bone microstructures with varying bone volume fraction are generated using a topology optimization-based bone microstructure reconstruction scheme. The obtained FE models of the trabecular bone were then used to develop a hybrid discrete/finite element model able to simulate the propagation of highly nonlinear solitary waves in a vertical array of steel particles, and their interaction with the adjacent bone microstructure model was studied. Two test modes were considered, one where the granular chain was placed in direct contact with the bone microstructure model, while in the second test mode, a face sheet was included between the chain and the bone model. For both test modes, we found that the characteristic features of the reflected solitary waves are sensitive to the effective compressive modulus of the bone microstructure models and follow similar trends than those obtained for a homogeneous, non-porous solid. It was also found that the use of the face sheet substantially reduces the sensitivity of the predictions to small changes in the bone topology, making it a robust and reliable method for non-destructive evaluation of the effective elastic modulus of cellular materials with small structural dimensions, as it is required for the site-specific evaluation of the mechanical properties of trabecular bone.

Ti6Al4V lightweight lattice structures manufactured by laser powder bed fusion for load-bearing applications

Additively manufactured (AM) lattice structures allow complex-shaped and custom parts, with superior design that cannot be produced by traditional methods. For medical implants, AM lattice structures are aimed at matching the elastic modulus of bone while providing strength and allowing bone in-growth for long-term stability. In this study, relatively thick struts are investigated in an attempt to match the properties of cortical bone, which is meant for the internal structural integrity of the implant, while a smaller lattice may be used for near-surface parts of an implant. In this work we investigate additively manufactured lattice samples produced by Laser Powder Bed Fusion (LPBF) of Ti6Al4V ELI, with samples having approximately 50% regular porosity. In particular, we experimentally compare two designs: diagonal and rhombic. MicroCT-based static loading simulations are used to highlight stress hotspots in the two designs, to highlight possible failure locations. Physical compression testing to initial failure and subsequent microCT highlight the locations of initial failure, which correlate well with the simulation stress hotspots. Both designs show excellent strength (120–140 kN failure load) and effective compressive elastic modulus corresponding well to simulations. Differences between microCT-based simulations of the produced lattices and those of ideal design parameters can be attributed mainly to surface roughness, and slightly thinner manufactured struts of the as-built lattices, with similar trends for the two model designs. These results validate experimentally that both designs are suitable for load-bearing applications.

Fabrication and characterization of auxetic shape memory composite foams

Shape memory polymers , as a kind of smart materials, play an important role in more and more fields, such as aerospace, biomedicine and intelligent clothing field and so on. Comparing with traditional materials, negative Poisson's ratio foam has excellent mechanical properties, such as double curvature, light weight, high shear resistance, auxetic etc., and it has a great potential application in the field of aerospace. Therefore, in this project, shape memory composite foam was fabricated based on the commercial soft polyurethane foam material as matrix and shape memory epoxy resin as functional phase. Negative Poisson's ratio of foam was fabricated based on its shape memory feature through a process of triaxial compression with heat treatment. Microstructure deformation was characterized after the transformation of auxetic foam. By adjusting the processing parameters, the auxetic shape memory foam with different “re-entrant” structure was obtained. Such fabricated shape memory composite foams display variable stiffness with auxetic behavior. Effective compressive and tensile modulus was obtained by compression and tension tests . The effect of processing parameters on foam Poisson's ratio was analyzed, which provided certain guiding significance for the further shape memory foam preparation.

Testing constitutive relations by running and walking on cornstarch and water suspensions.

The ability of a person to run on the surface of a suspension of cornstarch and water has fascinated scientists and the public alike. However, the constitutive relation obtained from traditional steady-state rheology of cornstarch and water suspensions has failed to explain this behavior. In another paper we presented an averaged constitutive relation for impact rheology consisting of an effective compressive modulus of a system-spanning dynamically jammed structure [R. Maharjan etal., this issue, Phys. Rev. E 97, 052602 (2018)10.1103/PhysRevE.97.052602]. Here we show that this constitutive model can be used to quantitatively predict, for example, the trajectory and penetration depth of the foot of a person walking or running on cornstarch and water. The ability of the constitutive relation to predict the material behavior in a case with different forcing conditions and flow geometry than it was obtained from suggests that the constitutive relation could be applied more generally. We also present a detailed calculation of the added mass effect to show that while it may be able to explain some cases of people running or walking on the surface of cornstarch and water for pool depths H>1.2 m and foot impact velocities V_{I}>1.7 m/s, it cannot explain observations of people walking or running on the surface of cornstarch and water for smaller H or V_{I}.

Strains in trussed spine interbody fusion implants are modulated by load and design.

Titanium cages with 3-D printed trussed open-space architectures may provide an opportunity to deliver targeted mechanical behavior in spine interbody fusion devices. The ability to control mechanical strain, at levels known to stimulate an osteogenic response, to the fusion site could lead to development of optimized therapeutic implants that improve clinical outcomes. In this study, cages of varying design (1.00 mm or 0.75 mm diameter struts) were mechanically characterized and compared for multiple compressive load magnitudes in order to determine what impact certain design variables had on localized strain. Each cage was instrumented with small fiducial sphere markers (88 total) at each strut vertex of the truss structure, which comprised of 260 individual struts. Cages were subjected to a 50 N control, 1000 N, or 2000 N compressive load between contoured loading platens in a simulated vertebral fusion condition, during which the cages were imaged using high-resolution micro-CT. The cage was analyzed as a mechanical truss structure, with each strut defined as the connection of two vertex fiducials. The deformation and strain of each strut was determined from 50 N control to 1000 N or 2000 N load by tracking the change in distance between each fiducial marker. As in a truss system, the number of struts in tension (positive strain) and compression (negative strain) were roughly equal, with increased loads resulting in a widened distribution (SD) compared with that at 50 N tare load indicating increased strain magnitudes. Strain distribution increased from 1000 N (+156 ± 415 με) to 2000 N (+180 ± 605 με) in 1.00 mm cages, which was similar to 0.75 mm cages (+132 ± 622 με) at 1000 N load. Strain amplitudes increased 42%, from 346με at 1000 N to 492με at 2000 N, for 1.00 mm cages. At 1000 N, strain amplitude in 0.75 mm cages (481με) was higher by 39% than that in 1.00 mm cages. These amplitudes corresponded to the mechanobiological range of bone homeostasis+formation, with 63 ± 2% (p < .05 vs other groups), 72 ± 3%, and 73 ± 1% of struts within that range for 1.00 mm at 1000 N, 1.00 mm at 2000 N, and 0.75 mm at 1000 N, respectively. The effective compressive modulus for both cage designs was also dependent on strut diameter, with modulus decreasing from 12.1 ± 2.3 GPa (1.25 mm) to 9.2 ± 7.5 GPa (1.00 mm) and 3.8 ± 0.6 GPa (0.75 mm). This study extended past micro-scale mechanical characterization of trussed cages to compare the effects of design on cage mechanical behavior at moderate (1000 N) and strenuous (2000 N) load levels. The findings suggest that future cage designs may be modulated to target desired mechanical strain regimes at physiological loads.

Design of an underwater acoustic bend by pentamode metafluid.

In this paper, an impedance matching underwater acoustic bend with pentamode microstructure is designed. The proposed bend is assembled by pentamode lattice. The effective density and compressive modulus of each unit cell can be tuned simultaneously, which are modulated to guarantee both the bending effect and high transmission. The standard deviations (SDs) of transmitted phase are calculated to quantitatively evaluate the degree of the distortion of the transmitted wavefront, while the transmission is calculated to appraise the degree of acoustic impedance matching. The low SDs and high transmission indicate that the designed bend has a nice broadband bending effect and is impedance-matched to water. This design has potential applications in underwater communication and underwater detection.

Dynamic Regulation of Bone Morphogenetic Proteins in Engineered Osteochondral Constructs by Biomechanical Stimulation

Osteochondral tissue-engineered grafts are proposed to hold greater potential to repair/regenerate damaged cartilage through enhanced biochemical and mechanical interactions with underlying subchondral bone as compared to simple engineered cartilage. Additionally, biomechanical stimulation of articular chondrocytes (ACs) or osteoblasts (OBs) was shown to induce greater morphogenesis of the engineered tissues composed of these cells. In this report, to define the advantages of biomechanical stimulation to osteochondral grafts for tissue engineering, we examined whether (1) ACs and OBs in three-dimensional (3D) osteochondral constructs support functional development of each other at the molecular level, and (2) biomechanical stimulation of osteochondral constructs further promotes the regenerative potential of such grafts. Various configurations of cell/scaffold assemblies, including chondral, osseous, and osteochondral constructs, were engineered with mechano-responsive electrospun poly(ɛ-caprolactone) scaffolds. These constructs were subjected to either static or dynamic (10% cyclic compressive strain at 1 Hz for 3 h/day) culture conditions for 2 weeks. The expression of bone morphogenetic proteins (BMPs) was examined to assess the regenerative potential of each treatment on the cells. Biomechanical stimulation augmented a marked upregulation of Bmp2, Bmp6, and Bmp7 as well as downregulation of BMP antagonist, Bmp3, in a time-specific manner in the ACs and OBs of 3D osteochondral constructs. More importantly, the presence of biomechanically stimulated OBs was especially crucial for the induction of Bmp6 in ACs, a BMP required for chondrocytic growth and differentiation. Biomechanical stimulation led to enhanced tissue morphogenesis possibly through this BMP regulation, evident by the improved effective compressive modulus of the osteochondral constructs (710 kPa of dynamic culture vs. 280 kPa of static culture). Similar BMP regulation was observed in the femoral cartilages of the rats subjected to gentle exercise, demonstrating the physiological relevance of in vitro biomechanical stimulation of osteochondral constructs. Overall, our findings show that biomechanical stimulation may be critical for cross signaling between ACs and OBs to support chondrocytic growth in 3D osteochondral tissues.

The experimental measurement of effective compressive modulus of carbon nanotube forests and the nature of deformation

Measurement of the effective compressive modulus of vertically aligned carbon nanotube (CNT) forests/turfs is evaluated with two different experimental methods. The first experimental method uses a high force nanoindentation system to uniformly compress CNT forests grown on rigid silicon substrates with a second silicon substrate on the top surface of the CNTs. This is performed for CNTs with heights of 61, 315, and 683μm. Using this nanoindentation-based method, the measured effective compressive modulus values ranged from 0.12 to 1.2MPa. Additionally, the effect of end constraints is investigated by testing the CNT forests with and without attaching the second rigid substrate to the CNT forest tips with an adhesive. It was found that attaching the second substrate to the CNT tips with an adhesive increases the measured effective compressive modulus by 10–30%. The second experimental method in this study is semi in situ and uses a scanning electron microscope and a compressive fixture with load cell. This method shows that under uniform compressive loading, the CNT forests demonstrate a local folding form of deformation with initial folding occurring near the growth substrate. The effective compressive modulus measured using this method was 0.11MPa for 133μm tall CNT forests.

An experimental method to determine the resistance of a vertically aligned carbon nanotube forest in contact with a conductive layer

High density vertically aligned carbon nanotube (VACNT) forests are considered as a promising conductive material for many applications (interconnects in microelectronics or contact material layer in sliding contact applications). It is thus crucial to characterize the electrical resistance of these forests, especially in contact with the inherent top/bottom conductive substrates. This paper aims to develop an original method to determine the contribution of the different terms in this electrical resistance, which is measured with a tipless atomic force microscope used in high accuracy “force mode.” VACNT stacks with different heights on AlCu substrate with or without Au/Pd top coating are studied. The electrical contact area between the probe tip and the forest is considered to be equivalent to the classical electrical contact area between a tip and a rough surface. With this assumption, the scattering resistance of a mono-wall CNT is 14.6 kΩ μm−1, the top/bottom contact resistance is, respectively, 265 kΩ/385 kΩ. The bottom resistance divided in half is obtained by an interface substrate/CNT catalyst treatment. The same assumption leads to an effective compressive modulus of 175 MPa. These results are consistent with the values published by other authors. The proposed method is effective to optimise the CNT interface contact resistance before integration in a more complex functional structure.