Question

B. Indentation of a cell with an adhesive sphere. Consider the situation depicted in Figure 2. A compressive force F is applied by an adhesive sphere on an elastic half-space representing the surface of a cell. Our goal is to estimate to if Hertz model could still be used to establish the relationship between the force F and the indentation d, or if a model taking into account adhesion is unavoidable. R a d Figure 2. Adhesive contact between a sphere and an elastic half-plane. The JKR theory (JKR for Johnson, Kendall, and Roberts) takes into account adhesion between an indenter and an elastic body. It leads to the following relationship between the applied force Fand the contact radius a: 1/2 (8Wa3 F = E* E" where W is the adhesion energy (needed to be spent to detach the contact, in J/m²), E* = E the Youngn's modulus of the elastic plane and v is the Poisson's ratio of the elastic plane, and R the bead radius. ::))) R E tv2 with Q6. Calculate the ratio between the force given by the and the JKR theory and the Hertz theory.

Answer 1

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