Elastic contact to nearly incompressible coatings -- Stiffness enhancement and elastic pile-up

We have recently proposed an efficient computation method for the frictionless linear elastic axisymmetric contact of coated bodies [A. Perriot and E. Barthel, J. Mat. Res. 19 (2004) 600]. Here we give a brief description of the approach. We also discuss implications of the results for the instrumented indentation data analysis of coated materials. Emphasis is laid on incompressible or nearly incompressible materials (Poisson ratio $\nu>0.4$): we show that the contact stiffness rises much more steeply with contact radius than for more compressible materials and significant elastic pile-up is evidenced. In addition the dependence of the penetration upon contact radius increasingly deviates from the homogeneous reference case when the Poisson ratio increases. As a result, this algorithm may be helpful in instrumented indentation data analysis on soft and nearly incompressible layers

Determination of Young's modulus of samples of arbitrary thickness from force distance curves: numerical investigations and simple approximate formulae

We present simple expressions for load required to indent a layer of arbitrary thickness with a conical, paraboloidal or cylindrical punch. A rigid substrate underneath the sample leads to an increase of load required for indentation. This effect has to be corrected for to prevent overestimation of Young's modulus from indentation measurements, such as force - distance curves recorded with the Atomic Force Microscope (AFM). The problems of the frictionless contact of an axisymmetric punch and an isotropic, linear-elastic layer are reducible to Fredholm integral equations of the second kind. We solved them numerically and used the Remez algorithm to obtain piecewise polynomial approximations of the load - indentation relation for samples that are either in frictionless contact with the rigid substrate or bonded to it. Their relative error due to approximation is negligible and uniformly spread. Combining the numerical approximations with asymptotic solutions for very thin layers, we obtained equations appropriate for samples of arbitrary thickness. They were implemented in a new version of AtomicJ, our free, open source application for analysis of AFM recordings

An asymptotic model for a thin bonded elastic layer coated with an elastic membrane

The deformation problem for a transversely isotropic elastic layer bonded to a rigid substrate and coated with a very thin elastic layer made of another transversely isotropic material is considered. The leading-order asymptotic models (for compressible and incompressible layers) are constructed based on the simplifying assumptions that the generalized plane stress conditions apply to the coating layer, and the flexural stiffness of the coating layer is negligible compared to its tensile stiffness.Comment: 11 pages, 1 figur

Axisymmetric contact problem for a flattened cell : contributions of substrate effect and cell thickness to the determination of viscoelastic properties by using AFM indentation

Nanoindentation technology has proven an effective method to investigate the viscoelastic properties of biological cells. The experimental data obtained by nanoindentation are frequently interpreted by Hertz contact model. However, in order to facilitate the application of Hertz contact model, a mass of studies assume cells have infinite thickness which does not necessarily represent the real situation. In this study, a rigorous contact model based upon linear elasticity is developed for the interpretation of indentation tests of flattened cells which represent a factual morphology. The cell, normally bonded to the petri dish, is initially treated as an elastic layer of finite thickness perfectly fixed to a rigid substrate, and the conic indenter is assumed to be frictionless. The theory of linear elasticity is utilized to solve this contact issue and then the solutions are extended to viscoelastic situation which is regarded as a good indicator for mechanical properties of biological cells. To test the present model, an AFM-based creep test has been conducted on living human hepatocellular carcinoma cell (SMMC-7721 cell) and its fullerenol-treated counterpart. The results indicate that the present model could not only describe very well the creep behavior of SMMC-7721 cells, but can also curb overestimation of the mechanical properties due to substrate effect. Moreover, the present model could identify the difference between the control and treated SMMC-7721 cells in terms of the extracted viscoelastic parameters, suggesting its potential in revealing the biomechanical effects of fullerenol-like drug treatment on cancerous cells