Modified Hertz Model Research Articles

Mechanical characterization of multi-layered lipid nanoparticles using high-resolution AFM force spectroscopy

Lipid nanoparticles (LNPs) have been widely used in drug delivery systems. Their physicochemical properties play a substantial role in the pharmaceutical functions and therapeutic efficacy of encapsulated drugs. Although, numerous previous studies have examined the optimal physicochemical properties for drug delivery, the role of LNP mechanical compliance has not yet been established, owing to limitations imposed by their small size, extreme softness, and complex structures. The aim of this study was to delineate the true topography and the map of elastic moduli of LNPs by analyzing atomic force microscope (AFM) force spectroscopic data based on the modified Hertz model considering the asymptotic approach. Results reveal a hard core-soft shell structure of LNPs. Additionally, the elastic moduli of the core of LNPs are modulated from 176 kPa to 599 kPa through the addition of crosslinked alginate. However, a consistent elastic modulus (∼128 kPa) of outer shells is maintained regardless of core composition. In addition, Transwell assay show that, compared to rigid LNPs, those with soft properties exhibit enhanced permeation. This finding, which delineates the true topography and elastic moduli of LNPs, suggest an alternative for resolving the long-standing issues in AFM force spectroscopic studies.

Physical and Mechanical Characterization of Fibrin-Based Bioprinted Constructs Containing Drug-Releasing Microspheres for Neural Tissue Engineering Applications

Three-dimensional bioprinting can fabricate precisely controlled 3D tissue constructs. This process uses bioinks—specially tailored materials that support the survival of incorporated cells—to produce tissue constructs. The properties of bioinks, such as stiffness and porosity, should mimic those found in desired tissues to support specialized cell types. Previous studies by our group validated soft substrates for neuronal cultures using neural cells derived from human-induced pluripotent stem cells (hiPSCs). It is important to confirm that these bioprinted tissues possess mechanical properties similar to native neural tissues. Here, we assessed the physical and mechanical properties of bioprinted constructs generated from our novel microsphere containing bioink. We measured the elastic moduli of bioprinted constructs with and without microspheres using a modified Hertz model. The storage and loss modulus, viscosity, and shear rates were also measured. Physical properties such as microstructure, porosity, swelling, and biodegradability were also analyzed. Our results showed that the elastic modulus of constructs with microspheres was 1032 ± 59.7 Pascal (Pa), and without microspheres was 728 ± 47.6 Pa. Mechanical strength and printability were significantly enhanced with the addition of microspheres. Thus, incorporating microspheres provides mechanical reinforcement, which indicates their suitability for future applications in neural tissue engineering.

Evolution of surface roughness of single sand grains with normal loading

The surfaces of soil grains are not perfectly smooth, especially examined at small scale. In geotechnical engineering, surface roughness has been found to be able to influence the inter-particle friction angle at micro scale and small-strain stiffness at macro scale. However, the quantity and quality of the studies on surface roughness of natural soils are still limited. In this study, the evolution of surface roughness of natural sand grains with increasing normal load was investigated by a single-particle compression apparatus. Thirty Leighton Buzzard sand (LBS) grains coarser than 2·36 mm were tested, and the surface roughness was measured before and after compression by an optical interferometer. The deformations of the asperities and of the bulk of the sand grains in the vicinity of the contact were mapped. Three stages were identified as the normal load increased: (a) plastic deformation of the asperities; (b) asperities and bulk plastic deformation; and (c) bulk only plastic deformation. At very small normal load, only the asperities were found to deform plastically, and the surface roughness of the sand grains decreases due to the flattening of the asperities. Within this regime, the load–displacement relationship of LBS grains under compression could be simulated by the modified Hertz model, which takes surface roughness into consideration. With increasing normal load, the bulk of the sand grains began to yield near the contact. The geometry of the surfaces of LBS grains in contact with the loading platen is the main factor that influences the plastic deformation of the bulk. Differently from the plastic deformation of the asperities, the plastic deformation of the bulk could both smoothen and roughen the surfaces. When plastic deformation of the bulk occurred, both Hertz and modified Hertz theory could not predict the load and displacement relationship of sand grains. Through analysing the cumulative distributions of surface roughness of 30 LBS grains at different normal loads by the Weibull function, the surface roughness was found to decrease dramatically with increasing normal load at first and then tended to be constant.

A modified Hertz model for finite spherical indentation inspired by numerical simulations

In this paper, a modified Hertz model inspired by numerical simulations is proposed to predict the contact response of a linearly elastic half-space under finite spherical indentations. The proposed contact model presents a theoretical fundamental to measure the Young's moduli of the soft materials based on the finite indentation tests. The axisymmetric finite element (FE) model is created, and it is first applied to simulate the infinitesimal spherical indentations. The findings show that the FE simulation results agree well with those predicted by the classical Hertz model, which verifies that the FE model is accurate to simulate the contact responses. The FE model is then used to simulate the finite spherical indentions. Based on the numerical results of the finite spherical indentation up to the indenter radius, the radius of the contact zone is reformulated using the exact shape of the indenter, while the classical Hertz model uses a second-order approximation. This modified expression for the contact radius of the contact zone is then applied to reformulate the maximum contact pressure as well as the pressure distribution in the contact zone. After that, the reformulated pressure distribution is utilized to derive the contact force. The numerical results show that the modified Hertz model can predict very well the contact response of the linearly elastic half-space under the finite spherical indentations. The paradox whether the classical Hertz model can be extended to finite indentation is also clarified.

Contact control for grasping a non-cooperative satellite by a space robot

In this paper, the contact control problem of a space robot to grasp a non-cooperative satellite is investigated in detail, and a new capture control strategy is proposed. Firstly, the dynamic equation of the robot system is derived based on the multibody dynamics theory, and a modified Hertz model is used to describe the contact force between the robot end-effector and the target satellite. Then, a novel position-based impedance control strategy for capturing the target satellite is proposed. This control strategy is to capture the target satellite by realizing soft contact between the end-effector and the target satellite, thus the target satellite will not depart from the end-effector after their contact. Different from the other existing capture control strategies, the proposed strategy needs only the kinematic information of the space robot, so the control performance requirement is lower and is easier to implement in practice. To verify the validity of the proposed capture control strategy, simulations are conducted at the end of this paper, and the results indicate that the target satellite can be grasped effectively using the proposed capture control strategy if the motion of the target satellite is translational or tumbling.

A Novel Toolkit for Characterizing the Mechanical and Electrical Properties of Engineered Neural Tissues.

We have designed and validated a set of robust and non-toxic protocols for directly evaluating the properties of engineered neural tissue. These protocols characterize the mechanical properties of engineered neural tissues and measure their electrophysical activity. The protocols obtain elastic moduli of very soft fibrin hydrogel scaffolds and voltage readings from motor neuron cultures. Neurons require soft substrates to differentiate and mature, however measuring the elastic moduli of soft substrates remains difficult to accurately measure using standard protocols such as atomic force microscopy or shear rheology. Here we validate a direct method for acquiring elastic modulus of fibrin using a modified Hertz model for thin films. In this method, spherical indenters are positioned on top of the fibrin samples, generating an indentation depth that is then correlated with elastic modulus. Neurons function by transmitting electrical signals to one another and being able to assess the development of electrical signaling serves is an important verification step when engineering neural tissues. We then validated a protocol wherein the electrical activity of motor neural cultures is measured directly by a voltage sensitive dye and a microplate reader without causing damage to the cells. These protocols provide a non-destructive method for characterizing the mechanical and electrical properties of living spinal cord tissues using novel biosensing methods.

Q-Adaptive Control of the Nonlinear Dynamics of the Cantilever-Sample System of an Atomic Force Microscope

The article presents the control of the nonlinear dynamics of the cantilever-sample system of an atomic force microscope (AFM) by the combination of Q-control and model reference adaptive control, when the AFM operates in contact mode. In this mode the AFM is always in contact with the sample, being able to measure the topographic characteristics for different materials and structures at a nanometric scale. For this task, the AFM uses a cantilever with a micro tip at one end that explores the surface of the sample during scanning. During this process, the closed loop feedback control keeps the acting force on the cantilever beam constant, where the error between the reference and the output of the plant is equivalent to the topography of the sample. We know that the nonlinear dynamics of the cantilever beam system is complex, due to the different types of nonlinear forces that act. In the contact mode the interaction force is described by the modified Hertz model when the cantilever-sample distance is less than 0.2 nm. Here we use an approximate model of the interaction force to reduce the complexity of the model, which depends on the Q factor. The proposed method combine the adaptive control with the control Q, where the control Q allows to reduce the force of beam interaction cantilever-sample, reducing the probability of damage in the sample and in the micro tip due to permanent contact. The Q control is incorporated to the proposed method through the design of the reference model and also a design formula for the effective Q factor is obtained. As a result we have that the proposed control method is stable, showing good performance for different surfaces and reference inputs. The stability of the system is proved by the second Lyapunov method. To show the effectiveness of the proposed method a variety of simulations are presented. The proposed method is totally general and can be applied to any nonlinear complex system.

Low-velocity impact response of FG-GRC laminated beams resting on visco-elastic foundations

This paper presents an investigation on the low-velocity impact response of a functionally graded graphene reinforced composite (FG-GRC) laminated beam subjected to a transverse impact load. The beam is assumed to rest on visco-Pasternak foundations in thermal environments. Each layer of the laminated beam has the same thickness, but the volume fraction of graphene reinforcement for the layers may be different and vary along the thickness direction in a piece-wise functionally graded pattern. The temperature dependent material properties of graphene reinforced composites (GRCs) are estimated by an extended Halpin–Tsai model, where the graphene efficiency parameters are introduced and determined from the results of molecular dynamics (MD) simulations. The impactor that applies the impact load to the beam may act at any position of the beam for which the central impact is treated as a special case. The contact process follows a modified Hertz model. The linear motion equations of the FG-GRC laminated beam are established based on a higher-order shear deformation beam theory when the impact position is arbitrary, whereas the nonlinear motion equations are obtained only for the central impact case. The motion equations of the beam and the dynamic equation of the impactor are then solved simultaneously by the Runge–Kutta approach. The numerical results illustrate the influences of functionally graded graphene distribution, foundation stiffness, temperature variation and different impactor velocities on the central deflection of the FG-GRC laminated beam as well as the contact force between the beam and the impactor.

Investigation of articular cartilage structural and biomechanical properties by atomic-force microscopy

Purpose: Although Osteoarthritis (OA) is a painful disease, which leads to a low quality of life for the patient as well as to a high socioeconomic burden, a functional cure remains elusive. Gaining new insights into the onset and progression of the disease is crucial but limited by the lack of biological tools able to display detailed structural and biomechanical properties of healthy and pathological cartilage. However, the cartilaginous ultrastructure and its mechanical properties are key factors for the overall functionality of the joint and should be considered as unique biomarkers of cartilage health status. The direct correlation of OA parameters, analyzed by histology and the OARSI scoring system, with cartilage structural and biomechanical properties assessed by atomic-force microscopy (AFM), will give new insights into the mechanisms underlying OA pathogenesis, into the impact of individual ECM molecules, and into disease progression. Methods: Paraffin embedded hind limbs, collected from euthanized wildtype mice (C57BL/6J), were dewaxed, re-hydrated and sectioned. AFM measurements were carried out using a BioScope Catalyst (Bruker) in combination with an inverse optical microscope (Zeiss LSM 150 Meta). For contact mode imaging and indentation-type AFM silicon nitride cantilevers with a nominal spring constant of 100 mN/m and integrated pyramidal tips with nominal radius of 20 nm were used. Images were recorded in air with a resolution of 512 × 512 pixels at a line rate of 1 Hz. After recording an overview image of the articular cartilage (AC), the scan area was reduced to obtain structural details within the ECM of the superficial layer. After AFM imaging, PBS at pH 7.4 was added to the sample for indentation measurements. Young's modulus was extracted from the approach force-distance curves using a modified Hertz model for a pyramidal indenter. Results: First measurements show that, with the help of AFM, we are able to image cartilage overall structure, collagen fibril orientation and D-band structure, as well as to measure tissue biomechanical properties on deparaffinized tissue sections. Indentation measurements demonstrate differences in the biomechanical properties of the outermost superficial layer to its adjacent middle zone as well as to the pericellular matrix of AC chondrocytes. Conclusions: Although cartilage biomechanical properties will change due to tissue fixation and paraffinization, our measurements on deparaffinized tissue sections are comparable to other AFM studies in the literature, which show similar trends in cartilage biomechanical properties, such as the reduced stiffness of the pericellular matrix of chondrocytes, in cartilage explants or cryo-sections. Our next step is to perform AFM measurements on different murine OA model (e.g. DMM and ageing models) using depraffinized tissue sections. The comparison of cartilage OARSI scoring and other staining methods such as IHC for OA markers, to the ultrastructure and biomechanical properties of cartilage using sections from the same animal and joint, will allow us to directly compare these parameters and gain new insights into the onset and progression of OA.

Nonlinear low-velocity impact response of FG-GRC laminated plates resting on visco-elastic foundations

Abstract The nonlinear transient response of functionally graded graphene reinforced composite (FG-GRC) laminated plates resting on visco-Pasternak foundations in thermal environments under impact load is investigated in this paper. Each layer of a laminated plate is assumed to have the same thickness, but the volume fraction of graphene is assumed to be functionally graded in a piece-wise pattern along the plate thickness direction. The stiffness of FG-GRC is then obtained by an extended Halpin-Tsai model, where the graphene efficiency parameters are introduced and determined by molecular dynamics (MD) simulations. The impactor is assumed to be a metal sphere and the contact process between the impactor and the laminated plate is described by a modified Hertz model. The effects of the visco-Pasternak foundation and the temperature variation as well as the initial load are taken into consideration. In the framework of von Karman type of kinematic nonlinearity, the motion equations of an FG-GRC laminated plate are established based on a higher-order shear deformation theory and solved by a two-step perturbation technique. Finally, the motion equations of the impactor and the FG-GRC laminated plate can be simultaneously solved by the Runge-Kutta approach. The numerical results illustrate the effects of functionally graded graphene distribution, foundation stiffness, temperature variation, initial in-plane load and different impactor velocities on the contact force and the deflection of the FG-GRC laminated plate.

Nonlinear low-velocity impact analysis of matrix cracked hybrid laminated plates containing CNTRC layers resting on visco-Pasternak foundation

Abstract This paper investigates the low-velocity impact response of a shear deformable laminated plate which contains both carbon nanotube reinforced composite (CNTRC) layers and fiber reinforced composite (FRC) layers. The effect of matrix cracks is considered and a refined self-consistent model (SCM) is selected to describe the degraded stiffness of the plate. The material properties of both FRC layers and CNTRC layers are assumed to be temperature-dependent. The plate rests on a visco-Pasternak foundation in thermal environments. A modified Hertz model is utilized to describe the contact force between the impactor and the plate. Based on a higher order shear deformation theory and von Karman nonlinear strain-displacement relationships, the motion equations of the plate are established and solved by means of a two-step perturbation approach. The effects of the crack density, CNT volume fraction, temperature variation and the foundation stiffness on the nonlinear low-velocity impact response of hybrid laminated plates with multiple matrix cracks are discussed in detail.

Texture-driven elastohydrodynamic bouncing

We investigate in detail the dynamics of bouncing of a fluid-immersed solid sphere onto a textured wall at moderate Reynolds and Stokes numbers. Using high-frequency interferometric measurements, the dynamics of the sphere is resolved in time and space, before, during and after collision with the wall. The critical Stokes number for bouncing is shown to be significantly influenced by the geometry of the texture, i.e. the surface fraction and the height of the micro-pillars. A modified Hertz model is developed to take into account the influence of this texture geometry on the collision dynamics. The predicted scaling for the collision time and penetration depth of the sphere into the textured wall is found to be in good agreement with the experimental measurements.

Cell confluency modulates cortical stiffness of human bone marrow endothelial cells (696.3)

Little is known about mechanical properties of human bone marrow endothelial cells (HBMEC) as culture conditions change. Here, we used atomic force microscopy (AFM) to test the hypothesis that the degree of confluency modifies HBMEC stiffness. Individual cells were compared in non‐confluent and confluent phases. Two HBMEC lines HBME‐1 and HBMEC‐60 immortalized by different methods were cultured until reaching a desired growth phase. Primary HBMEC were used as a reference. Cell stiffness was calculated as Young’s Moduli using a modified Hertz model from AFM cell‐surface force curves. Actin expression was analyzed by immunofluorescence and western blotting (WB). Young’s Moduli were significantly increased in confluent vs non‐confluent HBME‐1 (6.79±2.58 vs 4.73±1.78 kPa, p<0.01) and HBMEC‐60 (4.25±1.14 vs 2.03±1.09 kPa, p<0.01) cells. Non‐confluent HBME‐1 exhibited similar stiffness to the primary HBME (5.49±2.06 kPa). Topographical images revealed denser networks of actin stress fibers in confluent cells. F‐actin labeling confirmed these results. WB data indicated elevated pan‐actin levels in confluent HBMEC. Thus, HBMEC stiffness is influenced by cell confluency in culture and enhanced stiffness is associated with increased actin expression, a major cytoskeletal component contributing to cell mechanical properties.Grant Funding Source: Supported by NIH Grants HL095486 (GAM), CA160461 (VVG), VA BLR&D Service Award 1I01BX000609 (VVG)

Self-Reinforcement of PNIPAm–Laponite Nanocomposite Gels Investigated by Atom Force Microscopy Nanoindentation

Strain hardening and self-reinforcement were observed from poly(N-isopropylacrylamide)(PNIPAm)-Laponite nanocomposite hydrogels (NC gel) after large deformation of either stretching or tearing. These phenomena were investigated with atomic force microscopy (AFM) nanoindentation in nanoscale for the first time. Strong attractive force was detected from the indentation force curve of the as-prepared and swollen NC gels due to the capillary effect of water between the AFM tip and gel surface. The Young’s modulus E of the NC gels was evaluated by the AFM nanoindentation using the modified Hertz model, which increased with increasing laponite and decreased after swelling. After the NC gels suffered stretching to 900% strain or tearing to break, the Young’s modulus was substantially increased, implying the self-reinforcement of the gel samples. This effect was enhanced by increasing clay content. On relaxation of deformed samples containing a small amount of clay, the modulus almost recovered its original value...

An Improved Contact Model for Pounding Simulation of Base-isolated Highway Bridge

A modified Hertz model with nonlinear damping (Hertz damp model) is proposed for capturing the seismic pounding response of adjacent structures. Relevant parameters in the model are theoretically derived and numerically verified. Then, this model is used to simulate pounding response of a base-isolated highway bridge subjected to near fault ground motions. At the same time, nonlinear viscous dampers are installed between bridge decks for pounding prevention. The appropriate damping coefficient of the dampers can be found by parametric studies. It is shown that nonlinear viscous dampers are effective in reducing the relative displacement between bridge decks. At last, the hysteresis curve, the maximal damper force and stroke are used to demonstrate the behavior of nonlinear viscous dampers. The results indicate that satisfied viscous dampers can be produced to eliminate pounding according to the current manufacturing skills.

Local rheology of human neutrophils investigated using atomic force microscopy.

During the immune response, neutrophils display localized mechanical events by interacting with their environment through the micro-vascular transit, trans-endothelial, and trans-epithelial migration. Nano-mechanical studies of human neutrophils on localized nano-domains could provide the essential information for understanding their immune responsive functions. Using the Atomic Force Microscopy (AFM)-based micro-rheology, we have investigated rheological properties of the adherent human neutrophils on local nano-domains. We have applied the modified Hertz model to obtain the viscoelastic moduli from the relatively thick body regions of the neutrophils. In addition, by using more advanced models to account for the substrate effects, we have successfully characterized the rheological properties of the thin leading and tail regions as well. We found a regional difference in the mechanical compliances of the adherent neutrophils. The central regions of neutrophils were significantly stiffer (1,548 ± 871 Pa) than the regions closer to the leading edge (686 ± 801 Pa), while the leading edge and the tail (494 ± 537 Pa) regions were mechanically indistinguishable. The frequency-dependent elastic and viscous moduli also display a similar regional difference. Over the studied frequency range (100 to 300 Hz), the complex viscoelastic moduli display the partial rubber plateau behavior where the elastic moduli are greater than the viscous moduli for a given frequency. The non-disparaging viscous modulus indicates that the neutrophils display a viscoelastic dynamic behavior rather than a perfect elastic behavior like polymer gels. In addition, we found no regional difference in the structural damping coefficient between the leading edge and the cell body. Thus, we conclude that despite the lower loss and storage moduli, the leading edges of the human neutrophils display partially elastic properties similar to the cell body. These results suggest that the lower elastic moduli in the leading edges are more favorable for the elastic fluctuation of actin filaments, which supports the polymerization of the actin filaments leading to the active protrusion during the immune response.

Variations in the nanomechanical properties of virulent and avirulent Listeria monocytogenes

Atomic force microscopy (AFM) was used to quantify both the nanomechanical properties of pathogenic (ATCC 51776 & EGDe) and non-pathogenic (ATCC 15313 & HCC25) Listeria monocytogenes strains and the conformational properties of their surface biopolymers. The nanomechanical properties of the various L. monocytogenes strains were quantified in terms of Young's moduli of cells. To estimate Young's moduli, the classic Hertz model of contact mechanics and a modified version of it that takes into account substrate effects were used to fit the AFM nanoindentation-force measurements collected while pushing onto the bacterial surface biopolymer brush. When compared, the classic Hertz model always predicted higher Young's moduli values of bacterial cell elasticity compared to the modified Hertz model. On average, the modified Hertz model showed that virulent strains are approximately twice as rigid (88.1 ± 14.5 KPa) as the avirulent strains (47.3 ± 7.6 kPa). To quantify the conformational properties of L. monocytogenes' strains surface biopolymers, two models were used. First, the entropic-based, statistical mechanical, random walk formulation, the wormlike chain (WLC) model was used to estimate the elastic properties of the bacterial surface molecules. The WLC model results indicated that the virulent strains are characterized by a more flexible surface biopolymers as indicated by shorter persistence lengths (L(p) = 0.21 ± 0.08 nm) compared to the avirulent strains (L(p) = 0.24 ± 0.14 nm). Second, a steric model developed to describe the repulsive forces measured between the AFM tip and bacterial surface biopolymers indicated that the virulent strains are characterized by crowded and longer biopolymer brushes compared to those of the avirulent strains. Finally, scaling relationships developed for grafted polyelectrolyte brushes indicated L. monocytogenes strains' biopolymer brushes are charged. Collectively, our data indicate that the conformational properties of the bacterial surface biopolymers and their surface densities play an important role in controlling the overall bacterial cell elasticity.

Mechanical properties of zona pellucida hardening

We have investigated the changes in the mechanical properties of the zona pellucida (ZP), a multilayer glycoprotein coat that surrounds mammalian eggs, that occur after the maturation and fertilization process of the bovine oocyte by using atomic force spectroscopy. The response of the ZP to mechanical stress has been recovered according to a modified Hertz model. ZP of immature oocytes shows a pure elastic behavior. However, for ZPs of matured and fertilized oocyte, a transition from a purely elastic behavior, which occurs when low stress forces are applied, towards a plastic behavior has been observed. The high critical force necessary to induce deformations, which supports the noncovalent long interaction lifetimes of polymers, increases after the cortical reaction. Atomic force microscopy (AFM) images show that oocyte ZP surface appears to be composed mainly of a dense, random meshwork of nonuniformly arranged fibril bundles. More wrinkled surface characterizes matured oocytes compared with immature and fertilized oocytes. From a mechanical point of view, the transition of the matured ZP membrane toward fertilized ZP, through the hardening process, consists of the recovery of the elasticity of the immature ZP while maintaining a plastic transition that, however, occurs with a much higher force compared with that required in matured ZP.

Evidence of elastic to plastic transition in the zona pellucida of oocytes using atomic force spectroscopy

We have investigated the mechanical properties of the zona pellucida (ZP), a multilayer glycoprotein coat that surrounds mammalian eggs, using atomic force spectroscopy. The response of the membrane to mechanical stress has been reconstructed using a modified Hertz model. The transition from elastic behavior, which occurs when low stress forces are applied (characterized by a Young’s modulus E=(22±5) kPa), toward plastic behavior is observed. The critical indentation necessary to induce plastic deformations occurs at δyield=(550±50) nm. This high critical value, corresponding to two ZP layers, well supports the noncovalent long lifetimes of interactions that take place between constituent glycoproteins.

Energy Dissipation in the AFM Elasticity Measurements

Nowadays, it is well established that changes of cell stiffness observed by atomic force microscopy are linked with the cell cytoskeleton. Its structural and functional alterations are underlying major diseases such as cancer, inflammation or neurodegenerative disorders. So far, the use of atomic force microscopy is mostly focused on the determination of the Young modulus using the modified Hertz model. It can quantitatively describe the elastic properties of living cells, however, its value is burdened by the fact that cells are neither isotropic nor homogeneous material. Often, during the atomic force microscopy measurements, the hysteresis between the loading and unloading curves are observed which indicates the dissipation of an energy. In our studies, the index of plasticity was introduced to enumerate such effect during a single loading–unloading cycle. As the results show, such approach delivers an additional parameter describing the mechanical state of cell cytoskeleton. The analysis was performed on test samples where the mechanical properties of the melanoma cells were changed by glutaraldehyde and cytochalasin D treatments. The non-treated cells were compared with fibroblasts.