In experiments that involve contact with adhesion between two surfaces, as found in atomic force microscopy or nanoindentation, two distinct contact force (P) vs. 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 that 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.

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 polyacrylamideand 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 matrix's 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.traction force microscopy | confocal microscopy | large deformations | neutrophil M echanical cues within the cellular microenvironment regulate numerous fundamental functions including cell adhesion, deformation, and generation of traction (1-6). Analysis of cellular force generation, and its role in regulating homeostasis across a variety of cellular phenotypes and experimental platforms, has received much attention over the last three decades (7-13). Experimental quantification of cellular forces has produced several cell traction measurement techniques, ranging from surface wrinkle detection and flexure of micropillars to traction force microscopy (TFM) (12,(14)(15)(16)(17)(18)(19)(20). In TFM, measured cell-induced displacements are converted into tractions using various mathematical frameworks (14,15,17,18,21,22). Both twoand 3D TFM techniques have steadily increased in sophistication and now feature high-spatial displacement resolution and advanced computational formalisms to connect this displacement information to complex material constitutive laws (17,23,24).To successfully perform TFM, it is critical to know the stressstrain constitutive behavior of the matrix surrounding the cell. Although many TFM substrates feature relatively simple artificial gel constructs, such as polyacrylamide and polyethylene glycol, these constructs are impenetrable by cells and obviate measures obtained while cells are in a 3D setting (as would be the case within a bodily ...

No abstract

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 from numerical (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.

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. structure-property relationship | structural biomaterial | biocomposite | variational analysis B iological structural materials such as nacre, tooth, bone, and fish scales (1-9) often exhibit remarkable mechanical properties, which can be directly attributed to their unique structure and composition (10)(11)(12)(13)(14)(15). Through the detailed analysis of these complex skeletal materials, useful design lessons can be extracted that can be used to guide the synthesis of synthetic constructs with novel performance metrics (16)(17)(18)(19)(20). The complex and mechanically robust cage-like skeletal system of the hexactinellid sponge Euplectella aspergillum has proved to be a particularly useful model system for investigating structure-function relationships in hierarchically ordered biological composites (21-25). The sponge is anchored to the sea floor by thousands of anchor spicules (long, hair-like skeletal elements), each of which measures ca. 50 μm in diameter and up to 10 cm in length ( Fig. 1 A and B). The distal end of each anchor spicule is capped with a terminal crown-like structure and is covered with a series of recurved barbs that secure the sponge into the soft sediments of the sea floor (Fig. 1C). The proximal regions of these spicules are in turn bundled together and cemented to the main vertical struts of the skeletal lattice.These spicules contain an elastically heterogeneous, lamellar internal structure and are composed of amorphous hydrated silica. Surrounding a thin ...

No abstract

Contact force–indentation depth measurements in contact experiments involving compliant materials, such as polymers and gels, show a hysteresis loop whose size depends on the maximum indentation depth. This depth-dependent hysteresis (DDH) is not explained by classical contact mechanics theories and was believed to be due to effects such as material viscoelasticity, plasticity, surface polymer interdigitation, and moisture. It has been observed that the DDH energy loss initially increases and then decreases with roughness. A mechanics model based on the occurrence of adhesion and roughness related small-scale instabilities was presented by one of the authors for explaining DDH. However, that model only applies in the regime of infinitesimally small surface roughness, and consequently it does not capture the decrease in energy loss with surface roughness at the large roughness regime. We present a new mechanics model that applies in the regime of large surface roughness based on the Maugis–Dugdale theory of adhesive elastic contacts and Nayak’s theory of rough surfaces. The model captures the trend of decreasing energy loss with increasing roughness. It also captures the experimentally observed dependencies of energy loss on the maximum indentation depth, and material and surface properties.

The layered architecture of stiff biological materials often endows them with surprisingly high fracture toughness in spite of their brittle ceramic constituents. Understanding the link between organic-inorganic layered architectures and toughness could help to identify new ways to improve the toughness of biomimetic engineering composites. We study the cylindrically layered architecture found in the spicules of the marine sponge Euplectella aspergillum. We cut micrometer-size notches in the spicules and measure their initiation toughness and average crack growth resistance using flexural tests. We find that while the spicule's architecture provides toughness enhancements, these enhancements are relatively small compared to prototypically tough biological materials, like nacre. We investigate these modest toughness enhancements using computational fracture mechanics simulations.