Question

Dimitriadis et al. (Dimitriadis et al., Biophysical Journal 82(5) 2798–2810) have established a correction to the Hertz model for the indentation of a thin layer of thickness h and Young's modulus E, by a sphere R pressed with a force F. For an incompressible layer bonded to its substrate, the relationship between the compressive force Fand the indentation dis : ER1/2d3/2[1 + 1.133x + 1.283x2 +0.769x3 + 0.0975x4], Rd where x = aperta h Q10. Calculate the relative error e = F-FHertz if one were to use the Hertz model without correction, FHertz in the case where R = 2 um, d = 0.5 um, and h = 5 um. Does this error depend on E ? Conclude. Q11. Calculate e for R = 2 um, d = 0.2 um, and h = 1 um. Conclude.

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Answer 1

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