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.

[1]  S. BRODETSKY,et al.  Theory of Plates and Shells , 1941, Nature.

[2]  K. Kendall,et al.  Surface energy and the contact of elastic solids , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  D. Maugis,et al.  Fracture mechanics and the adherence of viscoelastic bodies , 1978 .

[4]  D. Maugis,et al.  Fracture Mechanics and Adherence of Viscoelastic Solids , 1980 .

[5]  William D. Nix,et al.  Analysis of the accuracy of the bulge test in determining the mechanical properties of thin films , 1992 .

[6]  Joost J. Vlassak,et al.  A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films , 1992 .

[7]  A. Ravve,et al.  Principles of Polymer Chemistry , 1995 .

[8]  Martin E. R. Shanahan,et al.  A novel test for the appraisal of solid/solid interfacial interactions , 1997 .

[9]  Adhesion of a punch to a thin membrane , 2000 .

[10]  K. Wan.  Adherence of an Axisymmetric Flat Punch on a Thin Flexible Membrane , 2001 .

[11]  Bharat Bhushan,et al.  Fundamentals of tribology and bridging the gap between the macro- and micro/nanoscales , 2001 .

[12]  K. Wan,et al.  Adherence of a Rectangular Flat Punch Onto a Clamped Plate: Transition From a Rigid Plate to a Flexible Membrane , 2002 .

[13]  K. Wan.  Adherence of an Axisymmetric Flat Punch Onto a Clamped Circular Plate: Transition From a Rigid Plate to a Flexible Membrane , 2002 .

[14]  K. Shull.  Contact mechanics and the adhesion of soft solids , 2002 .

[15]  R. Plaut,et al.  Effect of work of adhesion on contact of a pressurized blister with a flat surface , 2003 .

[16]  K. Wan,et al.  A theoretical and numerical study of a thin clamped circular film under an external load in the presence of a tensile residual stress , 2003 .

[17]  M. Saka,et al.  A systematic method for characterizing the elastic properties and adhesion of a thin polymer membrane , 2005 .

[18]  Xiangshan Chen,et al.  Plane-strain Bulge Test for Thin Films , 2005 .

[19]  K. Shull,et al.  Deformation and adhesive contact of elastomeric membranes , 2007 .

[20]  A. Jagota,et al.  Model-independent extraction of adhesion energy from indentation experiments. , 2008, Langmuir : the ACS journal of surfaces and colloids.

[21]  B. Nadler,et al.  Decohesion of a rigid punch from non-linear membrane undergoing finite axisymmetric deformation , 2008 .

[22]  K. Wan,et al.  Confined Thin Film Delamination in the Presence of Intersurface Forces With Finite Range and Magnitude , 2009 .

[23]  C. Jin.  Theoretical study of mechanical behavior of thin circular film adhered to a flat punch , 2009 .

[24]  A. Bower.  Applied Mechanics of Solids , 2009 .

[25]  C. Hui,et al.  Large deformation adhesive contact mechanics of circular membranes with a flat rigid substrate , 2010 .

[26]  Zhilong Peng,et al.  Effect of pre-tension on the peeling behavior of a bio-inspired nano-film and a hierarchical adhesive structure , 2012 .

[27]  Large deformation contact mechanics of a pressurized long rectangular membrane. II. Adhesive contact , 2013, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[28]  Jonathan T. Pham,et al.  Large deformation and adhesive contact studies of axisymmetric membranes. , 2013, Langmuir : the ACS journal of surfaces and colloids.