Parameters
Contact Model
Reduced modulus E* [GPa]
70.0 GPa
Glass:35 / Steel:115 / Si:100
Combined radius R [µm]
10.0 µm
Surface energy γ [mJ/m²]
50 mJ/m²
Applied load P [µN]
100 µN
Hardness H [GPa]
10.0 GPa
Display Mode
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Contact radius a [nm]
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Penetration δ [nm]
—
Peak pressure p₀ [GPa]
—
Pull-off force [µN]
—
Contact stiffness S
Theory
Hertz (elastic, no adhesion):
$$a = \left(\frac{3PR}{4E^*}\right)^{1/3},\quad \delta = \frac{a^2}{R},\quad p_0 = \frac{3P}{2\pi a^2}$$JKR (adhesion, compliant systems):
$$a^3 = \frac{R}{E^*}\left[P + 3\pi\gamma R + \sqrt{6\pi\gamma R P + (3\pi\gamma R)^2}\right]$$ $$F_{po}^{\mathrm{JKR}} = -\frac{3}{2}\pi\gamma R$$DMT (stiff systems):
$$F_{adh} = 2\pi\gamma R,\quad F_{po}^{\mathrm{DMT}} = -2\pi\gamma R$$Maugis parameter: $\mu_M < 0.1$ → DMT, $\mu_M > 5$ → JKR
Contact stiffness (Oliver-Pharr):
$$S = \frac{dP}{dh} = 2E^*\sqrt{\frac{A_c}{\pi}},\quad H = \frac{P_{max}}{A_c}$$
Applications: Rolling bearing contact fatigue / AFM and MEMS micro-adhesion analysis / Tire–road contact area estimation / Semiconductor CMP process design / Orthopedic implant bone-contact simulation.