Large deformation contact mechanics of long rectangular membranes. I. Adhesionless contact

In part I of this work, we study adhesionless contact of a long rectangular elastic membrane with a rigid substrate. Our model is based on finite strain theory and is valid for arbitrarily large deformations. Both frictionless and no-slip contact conditions are considered. Exact closed form solutions are obtained for frictionless contact. For small contact, the differences between these two contact conditions are small. However, significant differences occur for large contacts. For example, frictionless contact predicts a maximum pressure (and contact region) beyond which there is no solution; while the no-slip model places no restriction on both quantities. The effect of adhesion will be considered in part II of this work.