The axisymmetric boussinesq problem for a thick elastic layer under a punch of arbitrary profile

Dhaliwal, Ranjit S.; Rau, Indiresh S.

doi:10.1016/0020-7225(70)90086-8

Cited by 49 publications

(19 citation statements)

References 8 publications

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“…Dhaliwal and Rau presented a generalized analytical solution to the indentation problem of two bonded layers with different elastic properties ( Fig. 3A ) in the form of a Fredholm Integral Equation of the Second Kind 40 50 (see Eqs. 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 in the Materials and Methods section).…”

Section: Resultsmentioning

confidence: 99%

Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices

Staunton

Doss

Lindsay

et al. 2016

Sci Rep

132

102

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Mechanical interactions between cells and their microenvironment dictate cell phenotype and behavior, calling for cell mechanics measurements in three-dimensional (3D) extracellular matrices (ECM). Here we describe a novel technique for quantitative mechanical characterization of soft, heterogeneous samples in 3D. The technique is based on the integration of atomic force microscopy (AFM) based deep indentation, confocal fluorescence microscopy, finite element (FE) simulations and analytical modeling. With this method, the force response of a cell embedded in 3D ECM can be decoupled from that of its surroundings, enabling quantitative determination of the elastic properties of both the cell and the matrix. We applied the technique to the quantification of the elastic properties of metastatic breast adenocarcinoma cells invading into collagen hydrogels. We found that actively invading and fully embedded cells are significantly stiffer than cells remaining on top of the collagen, a clear example of phenotypical change in response to the 3D environment. Treatment with Rho-associated protein kinase (ROCK) inhibitor significantly reduces this stiffening, indicating that actomyosin contractility plays a major role in the initial steps of metastatic invasion.

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Section: Resultsmentioning

confidence: 99%

Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices

Staunton

Doss

Lindsay

et al. 2016

Sci Rep

132

102

View full text Add to dashboard Cite

show abstract

“…Historically, analytical expressions using integral transforms were derived to find the stress and displacement fields (Bufler 1971;Fretigny and Chateauminois 2000;Chen 1971). However, these methods still generally require sophisticated mathematical manipulations or extensive numerical computations (Tu and Gazis 1964;Dhaliwal and Rau 1970;Chen and Engel 1972). The inconvenience of using these solutions has largely precluded their use by experimentalists who need a simple solution to compare experiments to.…”

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confidence: 99%

Spherical indentation analysis of stress relaxation for thin film viscoelastic materials

Cheneler¹,

Mehrban²,

Bowen³

2013

Rheol Acta

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The mechanical testing of thin layers of soft materials is an important but difficult task. Spherical indentation provides a convenient method to ascertain material properties whilst minimising damage to the material by allowing testing to take place in situ. However, measurement of the viscoelastic properties of these soft materials is hindered by the absence of a convenient yet accurate model which takes into account the thickness of the material and the effects of the underlying substrate. To this end, the spherical indentation of a thin layer of viscoelastic solid material is analysed. It is assumed that the transient mechanical properties of the material can be described by the generalised standard linear solid model. This model is incorporated into the theory and then solved for the special case of a stress relaxation experiment taking into account the finite ramp time experienced in real experiments. An expression for the force as a function of the viscoelastic properties, layer thickness and indentation depth is given. The theory is then fitted to experimental data for the spherical indentation of poly(dimethyl)siloxane mixed with its curing agent to the ratios of 5:1, 10:1 and 20:1 in order to ascertain its transient shear moduli and relaxation time constants. It is shown that the theory correctly accounts for the effect of the underlying substrate and allows for the accurate measurement of the viscoelastic properties of thin layers of soft materials.

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“…This assumption might introduce significant errors in the determination of the Young's modulus of a cell (8). In fact, this concern has been considered in macroscopic measurements performed on thick layers (48) years before the invention of the AFM and its application to cell nanomechanics.…”

Section: Introductionmentioning

confidence: 99%

Determination of the Elastic Moduli of a Single Cell Cultured on a Rigid Support by Force Microscopy

García

2018

Biophysical Journal

115

129

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The elastic response of a living cell is affected by its physiological state. This property provides mechanical fingerprints of a cell's dysfunctionality. The softness (kilopascal range) and thickness (2-15 μm) of mammalian cells imply that the force exerted by the probe might be affected by the stiffness of the solid support. This observation makes infinite sample thickness models unsuitable to describe quantitatively the forces and deformations on a cell. Here, we report a general theory to determine the true Young's moduli of a single cell from a force-indentation curve. Analytical expressions are deduced for common geometries such as flat punches, paraboloids, cones, needles, and nanowires. For a given cell and indentation, the influence of the solid support on the measurements is reduced by using sharp and high aspect ratio tips. The theory is validated by finite element simulations.

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The axisymmetric boussinesq problem for a thick elastic layer under a punch of arbitrary profile

Cited by 49 publications

References 8 publications

Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices

Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices

Spherical indentation analysis of stress relaxation for thin film viscoelastic materials

Determination of the Elastic Moduli of a Single Cell Cultured on a Rigid Support by Force Microscopy

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