##### 2013 • Engineering and Technology

# Two Models of a Trapped Particle Between Adhering Surfaces

### Lead Presenter: Joel Parent

Micro and nanomechanics are growing fields in the semiconductor and related industries. Consequently obstacles, such as particles trapped between layers, are becoming more important and warrant further attention. This poster includes a numerical solution to the von Kàrmàn equations for moderately large deflection which is used to model a plate deformed due to a trapped particle lying between it and a rigid substrate. A model of a plastically deformed particle trapped between two elastic half-spaces will also be considered with a few pressure distributions in the area of the particle. Due to the small scales involved, the effect of adhesion is included. æThe recently developed moment-discontinuity method is used to relate the work of adhesion to the contact radius without the explicit need to calculate the total potential energy. For the von Kàrmàn model three different boundary conditions are considered the full clamp, the partial clamp and the compliant clamp. Curve-fit equations are found for the numerical solution to the non-dimensional coupled non-linear differential equations for moderately large deflections of an axisymmetric plate. These results are found to match the small deflection theory when the deflection is less than the plate thickness. æWhen the maximum deflection is much greater than the plate thickness, these results represent the membrane theory for which an approximate analytic solution exists.