Spatial Variation Of Stiffness Research Articles

Equine hoof wall: Structure, properties, and bioinspired designs

The horse hoof wall exhibits exceptional impact resistance and fracture control due to its unique hierarchical structure which contains tubular, lamellar, and gradient configurations. In this study, structural characterization of the hoof wall was performed revealing features previously unknown. Prominent among them are tubule bridges, which are imaged and quantified. The hydration-dependent viscoelasticity of the hoof wall is described by a simplified Maxwell-Weichert model with two characteristic relaxation times corresponding to nanoscale and mesoscale features. Creep and relaxation tests reveal that the specific hydration gradient in the hoof keratin likely leads to reduced internal stresses that arise from spatial stiffness variations. To better understand realistic impact modes for the hoof wall in-vivo, drop tower tests were executed on hoof wall samples. Fractography revealed that the hoof wall's reinforced tubular structure dominates at lower impact energies, while the intertubular lamellae are dominant at higher impact energies. Broken fibers were observed on the surface of the tubules after failure, suggesting that the physically intertwined nature of the tubule reinforcement and intertubular matrix improves the toughness of this natural fiber reinforced composite. The augmented understanding of the structure-mechanical property relationship in dynamic loading led to the design of additively manufactured bioinspired structures, which were evaluated in quasistatic and dynamic loadings. The inclusion of gradient structures and lamellae significantly reduced the damage sustained in drop tower tests, while tubules increased the energy absorption of samples tested in compact tension. The samples most similar to the hoof wall displayed remarkably consistent fracture control properties. Statement of significanceThe horse hoof wall, capable of withstanding large, repeated, dynamic loads, has been touted as a candidate for impact-resistant bioinspiration. However, our understanding of this biological material and its translation into engineered designs is incomplete. In this work, new features of the horse hoof wall are quantified and the hierarchical failure mechanisms of this remarkable material under near-natural loading conditions are uncovered. A model of the hoof wall's viscoelastic response, based on studies of other keratinous materials, was developed. The role of hydration, strain rate, and impact energy on the material's response were elucidated. Finally, multi-material 3D printed designs based on the hoof's meso/microstructure were fabricated and exhibited advantageous energy absorption and fracture control relative to control samples.

Combined AFM and super-resolution localisation microscopy: Investigating the structure and dynamics of podosomes

Podosomes are mechanosensitive attachment/invasion structures that form on the matrix-adhesion interface of cells and protrude into the extracellular matrix to probe and remodel. Despite their central role in many cellular processes, their exact molecular structure and function remain only partially understood. We review recent progress in molecular scale imaging of podosome architecture, including our newly developed localisation microscopy technique termed HAWK which enables artefact-free live-cell super-resolution microscopy of podosome ring proteins, and report new results on combining fluorescence localisation microscopy (STORM/PALM) and atomic force microscopy (AFM) on one setup, where localisation microscopy provides the location and dynamics of fluorescently labelled podosome components, while the spatial variation of stiffness is mapped with AFM. For two-colour localisation microscopy we combine iFluor-647, which has previously been shown to eliminate the need to change buffer between imaging modes, with the photoswitchable protein mEOS3.2, which also enables live cell imaging.

Generating realistic laminate fiber angle distributions for optimal variable stiffness laminates

The advent of advanced fiber placement technology has made it possible, through the use of fiber steering, to exploit the anisotropic properties of composite materials to a larger extent than was previously possible. Spatial variation of stiffness can be induced by steering composite fibers in curvilinear paths to give beneficial load and stiffness distribution patterns. Buckling of composite panels is one area where fiber steering has been proven to be very effective. Fiber angles and predefined fiber angle variations are used in most of the research on fiber steered composites reported in the literature, however, from an optimization point of view it is attractive to design such variable stiffness (VS) structures in terms of lamination parameters (LPs). This results in a two-step design approach. In the first step a VS composite is designed in terms of LPs, and in the second step the LPs are converted into fiber angle distributions for each layer in the laminate. A methodology is proposed to convert a known LP distribution for a VS composite laminate into a realistic design in terms of fiber angles, with minimum loss of structural performance, whilst satisfying a constraint on in-plane fiber angle curvature. The proposed conversion process is formulated as an optimization problem and can be used for any number of equi-thickness plies. The methodology was tested by converting a known optimal LP design for a sample structure, a square plate under bi-axial compression into a fiber angle design. The effect of the in-plane curvature constraint, the number of layers in the laminate, and the choice of objective function for the conversion process were studied for a balanced symmetric lay-up.

Modelling of parametric excitation of a flexible coupling–rotor system due to misalignment

A flexible diaphragm coupling, connecting two rotating shafts, is investigated for its dynamic characteristics, when subjected to parallel offset misalignment. The diaphragm coupling is a constant velocity coupling which becomes asymmetric once misaligned. Asymmetry creates directional difference or spatial variation of stiffness, as shown by a quasi-static finite element (FE) analysis using ABAQUS software. As the shafts rotate, this spatial variation in stiffness makes the diaphragm coupling–rotor system model to become time-varying. The time-varying direct and cross–coupled stiffness terms of the coupling are synthesized from the FE model and used in the governing equations of motion of the coupling–rotor system. This leads to a parametrically excited system due to the time-periodic stiffness coefficients of the coupling. Using Simulink, numerical integration has been performed to find the response of the system for both mass unbalance and inclination unbalance excitations that arise due to the tilt of the principal axes of the diaphragm due to parallel misalignment. The responses obtained clearly indicate the effect of parametric excitation at one-fourth, one-third, and one-half of the principal parametric resonance. To verify this model, an experimental setup has been developed for the coupling–rotor system model with misalignment. The experimental results clearly show the asymmetry between the two lateral direction responses, as predicted by the model.

On eigenvalue problem of bar structures with stochastic spatial stiffness variations

This paper presents an analysis of stochastic eigenvalue problem of plane bar structures. Particular attention is paid to the effect of spatial variations of the flexural properties of the structure on the first four eigenvalues. The problem of spatial variations of the structure properties and their effect on the first four eigenvalues is analyzed in detail. The stochastic eigenvalue problem was solved independently by stochastic finite element method (stochastic FEM) and Monte Carlo techniques. It was revealed that the spatial variations of the structural parameters along the structure may substantially affect the eigenvalues with quite wide gap between the two extreme cases of zero- and full-correlation. This is particularly evident for the multi-segment structures for which technology may dictate natural bounds of zero- and full-correlation cases.

Optimization of Variable-Stiffness Panels for Maximum Buckling Load Using Lamination Parameters

With the large-scale adoption of advanced fiber placement technology in industry, it has become possible to fully exploit the anisotropy of composite materials through the use of fiber steering. By steering the composite fibers in curvilinear paths, spatial variation of stiffness can be induced resulting in beneficial load and stiffness distribution patterns. One especially relevant area in which fiber steering has proved its effectiveness is in improving buckling loads of composite panels. Previous research used predefined forms of fiber angle variations and the coefficients of these analytic expressions were used as design variables. Alternatively, the local ply angles were used as design variables directly. In this paper, a framework is developed to treat the most general approach that considers the largest possible design space. The use of lamination parameters efficiently defines stiffness variation over a structural domain with the minimum number of variables. A conservative reciprocal approximation scheme is introduced. The inverse buckling factor is expanded linearly in terms of the in-plane stiffness and in terms of the inverse bending stiffness. The new approximation scheme is convex in lamination parameter space. Numerical results demonstrate improvements in excess of 100% in buckling loads of variable-stiffness panels compared to the optimum constant stiffness designs. Buckling load improvements are attributed primarily to in-plane load redistribution, which is confirmed both by the prebuckling stress distribution as well as by comparing the performance of designs optimized with variation of both in-plane and bending stiffness to those optimized with only bending stiffness variation. A tradeoff study between in-plane stiffness and buckling performance is also presented and shows the benefits of variable-stiffness design in enlarging the design possibilities of composite panels.