Large Indentation Research Articles

Sensing Biomechanical Alterations in Red Blood Cells of Type 1 Diabetes Patients: Potential Markers for Microvascular Complications

In physiological conditions, red blood cells (RBCs) demonstrate remarkable deformability, allowing them to undergo considerable deformation when passing through the microcirculation. However, this deformability is compromised in Type 1 diabetes mellitus (T1DM) and related pathological conditions. This study aims to investigate the biomechanical properties of RBCs in T1DM patients, focusing on identifying significant mechanical alterations associated with microvascular complications (MCs). We conducted a case-control study involving 38 T1DM subjects recruited from the Diabetes Care Unit at Fondazione Policlinico Gemelli Hospital, comprising 22 without MCs (control group) and 16 with MCs (pathological group). Atomic Force Microscopy was employed to assess RBC biomechanical properties in a liquid environment. We observed significant RBC stiffening in individuals with MCs, particularly during large indentations that mimic microcirculatory deformations. Univariate analysis unveiled significant differences in RBC stiffness (median difference 0.0006 N/m, p = 0.012) and RBC counts (median difference −0.39 × 1012/L, p = 0.009) between the MC and control groups. Bivariate logistic regression further demonstrated that combining these parameters could effectively discriminate between MC and non-MC conditions, achieving an AUC of 0.82 (95% CI: 0.67–0.97). These findings reveal the potential of RBC biomechanical properties as diagnostic and monitoring tools in diabetes research. Exploring RBC mechanical alterations may lead to the development of novel biomarkers, which, in combination with clinical markers, could facilitate the early diagnosis of diabetes-related complications.

Numerical analyses of spherical indenter intrusion into sandstone: From laboratory tests to numerical simulations

To explore the mechanical mechanisms of rock fracturing under compression during ball milling. The study investigates the effects of intrusion depth and indenter diameter on the evolution of stresses and plastic strains, integrating laboratory tests and numerical predictions. The results reveal a reduction in both axial and radial stresses with increasing intrusion depth into the rock. Shear stress experiences an initial rise followed by a decline, while circumferential stress demonstrates an initial increase followed by a rapid decrease in the radial direction. As the intrusion deepens, the predominant influence on plastic strain of rock shifts from shear stress dominance to a combined dominance of shear and circumferential stresses. The influence of the indenter diameter on the stress field diminishes following an exponential decay pattern. In terms of the plastic strain field, smaller indenters are more likely to induce plastic failure due to shear and circumferential stresses, larger indenters are more prone to plastic failure induced solely by shear stresses. As the number of indenters increases, the integration of the stress and plastic strain fields is enhanced. This implies that introducing more spherical indenters amplifies the collaborative effect, leading to a more cohesive fracturing of the rock.

Stress-Induced Martensitic Transformation in Na3YCl6.

Martensitic transformation with volume expansion plays a crucial role in enhancing the mechanical properties of steel and partially stabilized zirconia. We believe that a similar concept could be applied to unexplored nonoxide materials. Herein, we report the stress-induced martensitic transformation of monoclinic Na3YCl6 with an ∼3.4% expansion. In situ synchrotron X-ray diffraction and atomistic simulations showed that anisotropic crystallographic transformation from monoclinic to rhombohedral Na3YCl6 occurs exclusively under uniaxial pressure; no effect is observed under hydrostatic pressure conditions. The uniaxially pressed powder compact of monoclinic Na3YCl6 showed a large indentation impression and low Young's modulus, in contrast to its high bulk modulus, suggesting that these unique mechanical properties are induced by the martensitic transformation.

Towards Simpler Modelling Expressions for the Mechanical Characterization of Soft Materials

Aims: The aim of this paper is to develop a new, simple equation for deep spherical indentations. Background: The Hertzian theory is the most widely applied mathematical tool when testing soft materials because it provides an elementary equation that can be used to fit force-indentation data and determine the mechanical properties of the sample (i.e., its Young’s modulus). However, the Hertz equation is only valid for parabolic or spherical indenters at low indentation depths. For large indentation depths, Sneddon’s extension of the Hertzian theory offers accurate force-indentation equations, while alternative approaches have also been developed. Despite ongoing mathematical efforts to derive new accurate equations for deep spherical indentations, the Hertz equation is still commonly used in most cases due to its simplicity in data processing. Objective: The main objective of this paper is to simplify the data processing for deep spherical indentations, primarily by providing an accurate equation that can be easily fitted to force-indentation data, similar to the Hertzian equation Methods: A simple power-law equation is derived by considering the equal work done by the indenter using the actual equation. Results: The mentioned power-law equation was tested on simulated force-indentation data created using both spherical and sphero-conical indenters. Furthermore, it was applied to experimental force-indentation data obtained from agarose gels, demonstrating remarkable accuracy. Conclusion: A new elementary power-law equation for accurately determining Young’s modulus in deep spherical indentation has been derived.

Effects of adhesive and frictional contacts on the nanoindentation of two-dimensional material drumheads

Nanoindentation of suspended circular thin films, dubbed drumhead nanoindentation, is a widely adopted technique for characterizing the mechanical properties of micro- or nano-membranes, including atomically thin two-dimensional (2D) materials. This method involves suspending an ultrathin specimen over a circular microhole and applying a precise indenting force at the center using an atomic force microscope (AFM) probe. Classical solutions assuming a point load and a fixed edge, which are referred to as Schwerin-type solutions, are commonly used to estimate Young’s modulus of the membrane material out of load–deflection measurements. However, given the widespread experimental evidence for adhesive and frictional contacts between the probe tip and the membrane, as well as sliding between the membrane and its supporting substrate, quantitative investigations of the effects of these interactions are required. In this paper, we formulate a boundary value problem to rigorously model such effects, ensuring relevance to experimental operations. Our numerical analyses reveal that the adhesive effect at the tip-membrane interface diminishes as the indentation depth increases or the tip size decreases. Furthermore, frictional interactions at this interface shift the maximum membrane stress from the center to the tip-membrane contact line with increasing indentation depth and interfacial shear stress. At large indentation depths, the size of the indenter tip and the sliding of the membrane-substrate are found to have a large effect on the indentation load–deflection relationship. Thus, we propose a new approximate formula for this relationship assuming a non-adhesive and frictionless spherical tip of a finite radius and a slippery contact with the supporting substrate. This formula is more accurate than the widely used Schwerin-type solution. It can be used to simultaneously extract the in-plane stiffness of the membrane and the shear strength at the membrane-substrate interface.

Pressurized membranes between walls: Thermodynamic process changes force and stiffness

Pressurized solids are ubiquitous in nature. Mechanical properties of biological tissues arise from cell turgor pressure and membrane elasticity. Flat contact between cells generate nonlinear forces. In this work, cells are idealized as pressurized elastic membranes in frictionless contact with one another. Contact forces are experimentally measured on rubber-like membranes and computed using finite element analysis (FEA). FEA matches experimental force-indentation relationships from small to large indentations. With the chosen dimensionless numbers, data gather on a master curve. The isobaric force exhibits a 4/3 power law over 1.5 decades of indentation. Forces for other thermodynamic processes (adiabatic, isothermal/osmotic and isochoric) are interpolated from isobaric data. Regarding stiffness, the isochoric process is superlinear contrary to the sublinear isobaric stiffness. Simple force-indentation relationships are given for each process.

A Correction Function to Improve the Accuracy of Measuring Elastic Modulus by Instrumented Spherical Indentation

Abstract Instrumented indentation combined with the classic Oliver–Pharr method has been widely utilized to measure elastic modulus of various materials. However, the elastic modulus measured by instrumented spherical indentation (ISI) is not as accurate as that measured by instrumented sharp indentation, especially at large indentation depth. In this work, the effect of the maximum indentation depth on measurement of elastic modulus by ISI was deeply investigated through finite element simulations and experiments. It was found that errors in measured elastic moduli increase significantly due to the inaccurate estimation of contact radius and excessive increase in initial unloading stiffness as maximum indentation depth increases. A correction function was then proposed to correct the measured elastic modulus. After correction, the errors were effectively reduced to within ±5 % for most cases. This work contributes to discovery of the error source in the measurement of elastic modulus by ISI, thereby improving the measurement accuracy.

A Pressure Pulse‐Driven Transient Magnetospheric Event

AbstractBursty reconnection models predict that flux transfer events (FTEs) moving along the magnetopause launch fast mode compressional waves into the magnetosheath that push the bow shock outward. By contrast, increases in the solar wind density striking the bow shock should push that boundary inward and launch fast mode compressional waves that propagate across the magnetosheath, drive waves on the magnetopause, and generate transient events in the outer magnetosphere. Multipoint ACE, Wind, THEMIS, and GOES‐11/12 solar wind, bow shock, and magnetospheric observations on 14 October 2008 provide direct evidence for solar wind pressure pulses producing a large amplitude indentation with crater FTE‐like properties on the magnetopause.

Indentation of an elastic arch on a frictional substrate: Pinning, unfolding, and snapping.

In this study, we investigate the morphology and mechanics of a naturally curved elastic arch loaded at its center and frictionally supported at both ends on a flat, rigid substrate. Through systematic numerical simulations, we classify the observed behaviors of the arch into three configurations in terms of the arch geometry and the coefficient of static friction with the substrate. A linear theory is developed based on a planar elastica model combined with Amontons-Coulomb's frictional law, which quantitatively explains the numerically constructed phase diagram. The snapping transition of a loaded arch in a sufficiently large indentation regime, which involves a discontinuous force jump, is numerically observed. The proposed model problem enables a fully analytical investigation and demonstrates a rich variety of mechanical behaviors owing to the interplay among elasticity, geometry, and friction. This study provides a basis for understanding more common but complex systems, such as a cylindrical shell subjected to a concentrated load and simultaneously supported by frictional contact with surrounding objects.

Graphene oxide under the nanoscope: A comprehensive study of nanoindentation behavior

Graphene oxide membranes are expected to become one of the most important materials for technological applications due to their highly reactive surface, being directly related to their atomistic configuration. The understanding of its structure and physicochemical properties under mechanical deformation is becoming crucial in the development of new applications; however, the role of the different functional groups in the membrane and their response to external factors like indentation is still unclear. Nanoindentation experiments show elastic behavior when the penetration is small compared to the indenter radius and the membrane diameter. Molecular Dynamics simulations for large 3-layer graphene oxide membranes were carried out for a 50% oxidation content and the inclusion of epoxy and hydroxy groups. Simulations showed an elastic modulus similar to experimental values. After the elastic regime, the mechanical behavior is dominated by the evolution of functional groups. A quasi-elastic regime is uncovered, where unloading leads to self-healing of broken bonds. Finally, large indenter penetration leads to fracture, with fracture stress similar to experimental values.

Mechanical contribution of the pia-arachnoid complex to brain tissue revealed by large deformation indentation

Mechanical contribution of the pia-arachnoid complex to brain tissue revealed by large deformation indentation

Study of deformation behavior of plastic metal materials during laser-assisted micro-imprinting formings

When a large taper angle diamond taper indenter is used for micro-imprinting plastic metals, the stagnation zone is caused by excessive extrusion and friction within the material at the tip of the indenter, which in turn affects the flow characteristics of the material and the quality of the processed surface. In this study, the formation of laser-assisted diamond indenter micro-imprinting stagnation zone mechanism was proposed. The deformation behavior when processing plastic-metal materials using this technique is revealed by numerical simulation. And observed this phenomenon through the hardness distribution of the micro tapered hole cross-section. The results show that when the taper angle of the diamond indenter is greater than 105°, a significant stagnation zone occurs in the material. The initial morphology is jug-shaped, showing periodic changes due to the hard substrate. The average hardness in this region is 91.5 HV, which is significantly lower than the rest of the material. When P = 30 W, the height of the stagnation zone is reduced by 43 μm and the first presence time is extended by 90 μm. The reduction in the friction coefficient leads to a reduction in the width of the interfacial stagnation zone.

Indentation fracture of 4H-SiC single crystal

Understanding the deformation and fracture behavior of single crystal silicon carbide (SiC) under a single particle is of scientific and practical importance for the micromachining of single crystal SiC. In this work, we investigate the indentation fracture of a 4H-SiC single crystal wafer with the indentation direction perpendicular to (0001) plane, using Berkovich, Vickers, and Knoop indenters. All the indentations create radial cracks for the normal loads used in this work. Both the Vickers and Knoop hardness tests produce lateral cracks. The fracture toughness calculated from the Vickers hardness tests is smaller than the ones calculated from the Knoop hardness tests and the Berkovich indentations under large indentation loads. The fracture toughness of 4H-SiC single crystal decreases with the increase of the indentation load under small indentation loads for the Berkovich indentations, revealing the phenomenon of surface hardening. The surface energy calculated from the radial cracks is comparable to the results reported in the literature. We establish an analytical expression of the total energy dissipation of a single indentation cycle, including the contribution of indentation-induced cracking, which offers an approach to calculate the ratio of the energy dissipation due to cracking to the energy dissipation due to plastic deformation and determine the dominant deformation process controlling the indentation deformation. The analysis of the energy dissipation for the indentations of the 4H-SiC single crystal by the Berkovich indenter reveals that the energy dissipation from the indentation-induced cracking is significantly larger than (more than eight times) that from plastic deformation for the indentation loads larger than 75 mN.

Probing the Mechanical Properties of 2D Materials via Atomic-Force-Microscopy-Based Modulated Nanoindentation.

As the field of low-dimensional materials (1D or 2D) grows and more complex and intriguing structures are continuing to be found, there is an emerging need for techniques to characterize the nanoscale mechanical properties of all kinds of 1D/2D materials, in particular in their most practical state: sitting on an underlying substrate. While traditional nanoindentation techniques cannot accurately determine the transverse Young's modulus at the necessary scale without large indentations depths and effects to and from the substrate, herein an atomic-force-microscopy-based modulated nanomechanical measurement technique with Angstrom-level resolution (MoNI/ÅI) is presented. This technique enables non-destructive measurements of the out-of-plane elasticity of ultra-thin materials with resolution sufficient to eliminate any contributions from the substrate. This method is used to elucidate the multi-layer stiffness dependence of graphene deposited via chemical vapor deposition and discover a peak transverse modulus in two-layer graphene. While MoNI/ÅI has been used toward great findings in the recent past, here all aspects of the implementation of the technique as well as the unique challenges in performing measurements at such small resolutions areencompassed.

Microstructure evolution and mechanical behavior of magnetron sputtering AlN–Al nanostructured composite film

In this paper, a series of AlN–Al nanocomposite films are prepared by reactive magnetron sputtering. The effects of N2 flow rate on the microstructure and mechanical properties of the films are studied. The formation and evolution mechanism of the nanocomposite structure are revealed. The results show that with the decrease of N2 flow rate, the microstructure goes through three stages: pure AlN, amorphous Al surrounded nanocrystalline AlN and AlN nanoparticle reinforced Al matrix composite. Benefiting from the good wettability of Al on AlN ceramics, the film deposited at 6 sccm N2 flow rate forms a nanocomposite structure of about 8 nm AlN grains wrapped by 1–2 nm amorphous Al. The hardness of the films increases first and then decreases with the decrease of N2 flow rate, ranging from 4 GPa to 25 GPa. The toughness of the films is analyzed by the ratio of H/E, H3/E2, the normalized plastic depth (δH) and the morphology of large load indentation. The results show that the toughness of the nanocomposite film obtained at 6 sccm N2 flow rate is significantly improved while maintaining the hardness equivalent to that of pure AlN film. The improvement in toughness comes from the microcracks initiated in AlN hindered by the surrounding Al phase.

Edge effect and indentation depth-dependent contact behavior in contact of an elastic quarter-space

The edge effect in contact of an elastic quarter-space is numerically studied in this work. The extension of Hetényi’s approach of overlapping two elastic half-spaces is implemented in the boundary element method to obtain the solution of an elastic quarter-space whose top and side surfaces could be both loaded. In the study on the indentation test of a rigid sphere on an elastic quarter-space, the dependencies of the normal force, mean contact radius, and pressure distribution in contact area as well as the internal von Mises stress in relation to the position of the sphere from the side edge are obtained numerically and expressed by fitting the numerical results. These equations can be also used to interpret the indentation depth-dependent contact behavior: from Hertzian contact at the beginning of the indentation to the non-circular contact at large indentation depth.In addition, the results are compared with a contact case of a quarter-space in which the side surface of the quarter-space is not completely free: shear stresses on the side surface vanish but normal stress exists. The latter case generates very similar results, especially the contact area, but its solutions are much easier to achieve by applying a symmetrical loading on an elastic half-space, offering an effective way to approximate the solution of a quarter-space.

Investigation of mechanical and electronic properties of a novel quaternary transition-metal nitride Ti0.25W0.25V0.25Ta0.25N

Multi-element transition-metal nitrides possessing combinations of outstanding mechanical and physical properties have attracted increasing attention due to its potential applications. Here, a new transition-metal nitride alloying four metal elements of Ti, W, V and Ta is proposed, in which the doping ratios of these four metal elements are equal. Using an improved structure searching method, the potential structures with low enthalpies were fully explored. An orthorhombic structure was firstly disclosed and verified to be its ground-state phase. It is the most energetically favorable structure in the pressure of 0∼100 GPa. The phonon spectrum calculations demonstrated its lattice dynamical stability. Systematic study of its mechanical properties showed the orthorhombic structure not only possessed a large hardness of 32.4 GPa but also behaved a large indentation shear strength of about 30 GPa, greatly exceeding its well-known fcc-B1 phase (about 15 GPa). Meanwhile, we also compared the orthorhombic phase to its disordered structure within B1 phase by generating special quasirandom structures (SQS) with a 3 × 3 × 3 supercell (216 atoms), which can be viewed as its high-entropy phase. The results displayed this SQS system had comparable hardness and strength but greatly improved ductility and toughness relative to the ordered B1 phase.

Stress-strain curve mapping by nanoindentation – a technique to qualify diffusion-bonded window assemblies for ITER

The International Thermonuclear Experimental Reactor (ITER) is an international nuclear fusion research and engineering project with the aim to prove the feasibility of nuclear fusion as a large-scale carbon-free source of energy. The reactor vessel contains several diagnostic windows that provide a line of sight to the plasma. Design and qualification of such windows is challenging due to severe in-service conditions and the necessity to combine glasses with metals. One specific window is composed of fused silica glass that is connected to an Inconel ferrule via an aluminium bonding layer, where the joint is consolidated through a diffusion bonding process. The optimization of design and production process parameters of the windows is object of continuous improvements via dedicated three-dimensional finite element model (FEM) simulations. Importantly, these FEM simulations necessarily require stress-strain curves as input parameters. Such curves are difficult to obtain, especially from complex systems with dissimilar joints. In the present paper a methodology based on dynamic spherical nanoindentation has been developed and applied to map the stress-strain characteristics across the diffusion bonded joints. The methodology takes inspiration from the well-known theory to extract stress-strain curves from spherical nanoindentation. Here, it is applied to automated large indentation mapping with more than 1000 indentations including fully automated post-processing. The results provide bulk equivalent mechanical properties including yield stress, yield strain, work hardening parameters and elastic modulus at a micrometre resolution. Results show outstanding correlation with microstructural changes across the bonded cross-section, including grain refinement and twinning at the Inconel/aluminium interface.

Probing soft fibrous materials by indentation.

Indentation is often used to measure the stiffness of soft materials whose main structural component is a network of filaments, such as the cellular cytoskeleton, connective tissue, gels, and the extracellular matrix. For elastic materials, the typical procedure requires fitting the experimental force-displacement curve with the Hertz model, which predicts that f=kδ1.5 and k is proportional to the reduced modulus of the indented material, E/(1-ν2). Here we show using explicit models of fiber networks that the Hertz model applies to indentation in network materials provided the indenter radius is larger than approximately 12lc, where lc is the mean segment length of the network. Using smaller indenters leads to a relation between force and indentation displacement of the form f=kδq, where q is observed to increase with decreasing indenter radius. Using the Hertz model to interpret results of indentations in network materials using small indenters leads to an inferred modulus smaller than the real modulus of the material. The origin of this departure from the classical Hertz model is investigated. A compacted, stiff network region develops under the indenter, effectively increasing the indenter size and modifying its shape. This modification is marginal when large indenters are used. However, when the indenter radius is small, the effect of the compacted layer is pronounced as it changes the indenter profile from spherical towards conical. This entails an increase of exponent q above the value of 1.5 corresponding to spherical indenters. STATEMENT OF SIGNIFICANCE: The article presents a study of indentation in network biomaterials and demonstrates a size effect which precludes the use of the Hertz model to infer the elastic constants of the material. The size effect occurs once the indenter radius is smaller than approximately 12 times the mean segment length of the network. This result provides guidelines for the selection of indentation conditions that guarantee the applicability of the Hertz model. At the same time, the finding may be used to infer the mean segment length of the network based on indentations with indenters of various sizes. Hence, the method can be used to evaluate this structural parameter which is not easily accessible in experiments.

Free standing nanoindentation of penta-graphene via molecular dynamics: Mechanics and deformation mechanisms

The deformation and fracture mechanisms of penta-graphene under different loading conditions are still unclear and not thoroughly investigated. Hereby, the mechanical and transition/failure deformation properties of penta-graphene are investigated by using free standing nanoindentation techniques simulated via molecular dynamics. The indentation behaviors of penta-graphene under spherical and cylindrical indenters are compared and analyzed parametrically by considering the effects of the spherical/cylindrical indenter size, the loading rate and temperature. The results show that penta-graphene under spherical and cylindrical indentation exhibits unusual plastic deformation characteristics, which are consistent with those previously observed under uniaxial tensile and shear loading. The plastic deformation is originated from the pentagon-to-polygon structural transformation occurring at large indentation depths. The force at failure of the penta-graphene under spherical indenter is significantly lower than the one observed under cylindrical indenter; this is due to the small interaction area and high stress concentration caused by spherical indenter. We also identify the indentation parameters to accurately predict the mechanical parameters of penta-graphene using spherical or cylindrical indenters, and how these parameters influence the nanoindentation results. It is found that under both spherical and cylindrical indenter the Young's modulus of the penta-graphene is not sensitive to the loading rate, but generally decreases with the increasing temperature.