flat punch indentation
Indentation by an elliptical flat punch

This is a simple calculator for an elastic indentation by a flat punch.

Pressure profile can be calculated as follows:

 p(x,y) = p_0({1-\frac{x^2}{a^2} - \frac{y^2}{b^2}}^{-1/2})

where  p_0 = \frac{F_n}{2*\pi*a*b} ,  a being semi-major axis and  b being semi-minor axis,  F_n – normal load.

Indentation depth is calculated using following equation:

 \delta = \frac{F_n*K(e)}{\pi*E'*a} , where  K(e) is the complete elliptical integral of the first kind,  e=\sqrt{1-\frac{b^2}{a^2}} is eccentricity,  E' is the reduced elastic modulus,  1/{E'}= {1 - {\nu_1}^2}/{E_1} + {{\nu_2}^2}/{E_2} .

Equations are taken from [1].

Note: the elliptic integral of the first kind is required to calculate the indent value. An approximate formula is used here (http://www.exstrom.com/math/elliptic/ellipint.html).

 

[1]. J. Barber, Contact Mechanics, 2018.

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