Haneesh Kesari

Analytical solutions for the stiffness and damping coefficients of squeeze films in MEMS devices with perforated back plates

Closed-form expressions for the stiffness and the damping coefficients of a squeeze film are derived for MEMS devices with perforated back plates. Two kinds of perforation configurations are considered—staggered and matrix or non-staggered configuration. The analytical solutions are motivated from the observation of repetitive pressure patterns obtained fromnumerical (FEM) solutions of the compressible Reynolds equation for the two configurations using ANSYS. A single pressure pattern is isolated and further subdivided into circular pressure cells. Circular geometry is used based on observed symmetry. Using suitable boundary conditions, the Reynolds equation is analytically solved over the pressure cells. The complex pressure obtained is used to identify the stiffness and damping offered by the pressure cells. The stiffness and damping forces due to pressure cells within a pattern are added up separately. In turn, the stiffness and damping due to all the patterns are summed up resulting in the stiffness and damping forces due to the entire squeeze film. The damping and spring forces thus obtained analytically are compared with those obtained from the FEM simulations in ANSYS. The match is found to be very good. The regime of validity and limitations of the analytical solutions are assessed in terms of design parameters such as pitch to air gap, hole length to diameter and pitch to hole radius ratios. The analysis neglects inertial effects. Hence, the results are presented for low values of Reynolds number.

Role of Surface Roughness in Hysteresis during Adhesive Elastic Contact

In experiments that involve contact with adhesion between two surfaces, as found in atomic force microscopy or nanoindentation, two distinct contact force (P) versus indentation-depth (h) curves are often measured depending on whether the indenter moves towards or away from the sample. The origin of this hysteresis is not well understood and is often attributed to moisture, plasticity or viscoelasticity. Here we report experiments which show that hysteresis can exist in the absence of these effects, and that its magnitude depends on surface roughness. We develop a theoretical model in which the hysteresis appears as the result of a series of surface instabilities, in which the contact area grows or recedes by a finite amount. The model can be used to estimate material properties from contact experiments even when the measured P–h curves are not unique.

A new software tool (VA-BATTS) to calculate bending, axial, torsional and transverse shear stresses within bone cross sections having inhomogeneous material properties

Introduction: This study introduces, validates and demonstrates a new automated software tool (VA-BATTS) to calculate bone stresses within a bone cross section subjected to bending, axial, torsional and transverse shear far-field loading conditions, using quantitative computed tomography (QCT) data. Methods: A QCT image is imported and processed to generate a 2D finite element (FE) mesh of the bone with inhomogeneous (CT-based) transversely isotropic material properties. Bending and axial stresses are determined using inhomogeneous beam theory; torsional and transverse shear stresses are calculated using a new 2D FE formulation. Results: Validation studies show excellent agreement between results obtained using VA-BATTS and results obtained using analytical 2D models and inhomogeneous 3D FE models. Discussion: Out-of-plane bone stresses can be accurately calculated using a 2D analysis. Material inhomogeneity can have a marked effect on predicted stresses. In three-point bending experiments, transverse shear may present important contributions to the failure potential. The software is available at https://simtk.org/home/va-batts.

Mean deformation metrics for quantifying 3D cell–matrix interactions without requiring information about matrix material properties

Significance Investigations in mechanobiology rely on correlation of cellular processes with mechanical signals, such as matrix stiffness and cell tractions. Almost all cell traction and force quantification methodologies require knowledge of the underlying mechanical properties of the extracellular matrix to convert displacement data into corresponding traction data, which restricts the use of these techniques to systems in which the material properties are known. To overcome this hurdle, we present a new approach that does not require any knowledge of the underlying matrix properties but rather makes use of the intrinsically recorded kinematic displacement data. Through rigorous validation and an application to a neutrophil disease model, we show that such an approach produces both accurate and biologically significant information. Mechanobiology relates cellular processes to mechanical signals, such as determining the effect of variations in matrix stiffness with cell tractions. Cell traction recorded via traction force microscopy (TFM) commonly takes place on materials such as polyacrylamide- and polyethylene glycol-based gels. Such experiments remain limited in physiological relevance because cells natively migrate within complex tissue microenvironments that are spatially heterogeneous and hierarchical. Yet, TFM requires determination of the matrix constitutive law (stress–strain relationship), which is not always readily available. In addition, the currently achievable displacement resolution limits the accuracy of TFM for relatively small cells. To overcome these limitations, and increase the physiological relevance of in vitro experimental design, we present a new approach and a set of associated biomechanical signatures that are based purely on measurements of the matrixs displacements without requiring any knowledge of its constitutive laws. We show that our mean deformation metrics (MDM) approach can provide significant biophysical information without the need to explicitly determine cell tractions. In the process of demonstrating the use of our MDM approach, we succeeded in expanding the capability of our displacement measurement technique such that it can now measure the 3D deformations around relatively small cells (∼10 micrometers), such as neutrophils. Furthermore, we also report previously unseen deformation patterns generated by motile neutrophils in 3D collagen gels.

New functional insights into the internal architecture of the laminated anchor spicules of Euplectella aspergillum

Significance The remarkable properties of biological structural materials can often be attributed to the composite arrangement of their constituents. This paper focuses on the high-aspect-ratio, load-bearing, glassy skeletal fibers (spicules) of the marine sponge Euplectella aspergillum. Considering that the spicules’ internal architecture cannot be repaired or remodeled, we hypothesize that there is a connection between their internal structure and their strength. Using a newly developed structural mechanics model for composite beams, we demonstrate that the unique internal geometry that maximizes a beam’s strength correlates well with the geometry observed in the native spicules. This bio-inspired design strategy for increasing a beams strength has implications for a new generation of man-made structural materials. To adapt to a wide range of physically demanding environmental conditions, biological systems have evolved a diverse variety of robust skeletal architectures. One such example, Euplectella aspergillum, is a sediment-dwelling marine sponge that is anchored into the sea floor by a flexible holdfast apparatus consisting of thousands of anchor spicules (long, hair-like glassy fibers). Each spicule is covered with recurved barbs and has an internal architecture consisting of a solid core of silica surrounded by an assembly of coaxial silica cylinders, each of which is separated by a thin organic layer. The thickness of each silica cylinder progressively decreases from the spicule’s core to its periphery, which we hypothesize is an adaptation for redistributing internal stresses, thus increasing the overall strength of each spicule. To evaluate this hypothesis, we created a spicule structural mechanics model, in which we fixed the radii of the silica cylinders such that the force transmitted from the surface barbs to the remainder of the skeletal system was maximized. Compared with measurements of these parameters in the native sponge spicules, our modeling results correlate remarkably well, highlighting the beneficial nature of this elastically heterogeneous lamellar design strategy. The structural principles obtained from this study thus provide potential design insights for the fabrication of high-strength beams for load-bearing applications through the modification of their internal architecture, rather than their external geometry.

Significance of Nucleation Kinetics in Sn Whisker Formation

Sn whiskers are believed to form in response to stress in layers used as protective coatings. However, what makes them form at specific sites on the surface is not known. We have used thermal expansion mismatch to induce stress and observe the resulting whisker formation. Cross-sectional measurements of the region around whiskers show that there are oblique grain boundaries under the whiskers that are not seen in the as-deposited columnar structure. The kinetics also suggest that the whiskering sites may be formed by a nucleation process. Based on these results, we propose a nucleation mechanism in which the boundaries of the surrounding grains migrate due to strain energy differences and create oblique boundaries at which whiskers can form. A simple model is developed to predict the stress-dependence of the nucleation rate.

A new structure-property connection in the skeletal elements of the marine sponge Tethya aurantia that guards against buckling instability

We identify a new structure-property connection in the skeletal elements of the marine sponge Tethya aurantia. The skeletal elements, known as spicules, are millimeter-long, axisymmetric, silica rods that are tapered along their lengths. Mechanical designs in other structural biomaterials, such as nacre and bone, have been studied primarily for their benefits to toughness properties. The structure-property connection we identify, however, falls in the entirely new category of buckling resistance. We use computational mechanics calculations and information about the spicules’ arrangement within the sponge to develop a structural mechanics model for the spicules. We use our structural mechanics model along with measurements of the spicules’ shape to estimate the load they can transmit before buckling. Compared to a cylinder with the same length and volume, we predict that the spicules’ shape enhances this critical load by up to 30%. We also find that the spicules’ shape is close to the shape of the column that is optimized to transmit the largest load before buckling. In man-made structures, many strategies are used to prevent buckling. We find, however, that the spicules use a completely new strategy. We hope our discussion will generate a greater appreciation for nature’s ability to produce beneficial designs.

Effects of geometric nonlinearity in an adhered microbeam for measuring the work of adhesion

Design against adhesion in microelectromechanical devices is predicated on the ability to quantify this phenomenon in microsystems. Previous research related the work of adhesion for an adhered microbeam to the beams unadhered length, and as such, interferometric techniques were developed to measure that length. We propose a new vibration-based technique that can be easily implemented with existing atomic force microscopy tools or similar metrology systems. To make such a technique feasible, we analysed a model of the adhered microbeam using the nonlinear beam theory put forth by Woinowsky–Krieger. We found a new relation between the work of adhesion and the unadhered length; this relation is more accurate than the one by Mastrangelo & Hsu (Mastrangelo & Hsu 1993 J. Microelectromech. S., 2, 44–55. (doi:10.1109/84.232594)) which is commonly used. Then, we derived a closed-form approximate relationship between the microbeams natural frequency and its unadhered length. Results obtained from this analytical formulation are in good agreement with numerical results from three-dimensional nonlinear finite-element analysis.

A Millimeter Scale Flexural Testing System for Measuring the Mechanical Properties of Marine Sponge Spicules

Many load bearing biological structures (LBBSs)-such as feather rachises and spicules-are small (<1 mm) but not microscopic. Measuring the flexural behavior of these LBBSs is important for understanding the origins of their remarkable mechanical functions. We describe a protocol for performing three-point bending tests using a custom-built mechanical testing device that can measure forces ranging from 10-5 to 101 N and displacements ranging from 10-7 to 10-2 m. The primary advantage of this mechanical testing device is that the force and displacement capacities can be easily adjusted for different LBBSs. The devices operating principle is similar to that of an atomic force microscope. Namely, force is applied to the LBBS by a load point that is attached to the end of a cantilever. The load point displacement is measured by a fiber optic displacement sensor and converted into a force using the measured cantilever stiffness. The devices force range can be adjusted by using cantilevers of different stiffnesses. The devices capabilities are demonstrated by performing three-point bending tests on the skeletal elements of the marine sponge Euplectella aspergillum. The skeletal elements-known as spicules-are silica fibers that are approximately 50 µm in diameter. We describe the procedures for calibrating the mechanical testing device, mounting the spicules on a three-point bending fixture with a ≈1.3 mm span, and performing a bending test. The force applied to the spicule and its deflection at the location of the applied force are measured.