On the 150th Anniversary of Winkler’s Foundation: Its Profound Influence on the Fields of Mechanics and Adhesion Science

Wednesday, October 11, 2017

2:30pm - 3:45pm

107 Surge Building

David Dillard
Biomedical Engineering and Mechanics
Virginia Tech


Few advanced mechanics of materials solutions have found broader and more enduring applications than Emil Winkler’s beam on elastic foundation solution published in 1867.  With obvious initial applicability to rails supported by the earth, the essence of the model lies in the simple but profound assumption that the restoring force of an elastic foundation is linearly proportional to the deflection.  The important resulting solution has been applied to a wide range of engineering applications, including a plethora of discrete and continuous loading and boundary conditions, extensions to plates and pontoon bridges, and the analysis of deflections and stresses in pressurized cylindrical tanks.  Of particular interest has been the varied adaptations of this model to the field of adhesion, where it ranks with Volkersen’s 1937 shear lag concept in importance and versatility.  The long line of applications of the Winkler foundation to adhesion began with Goland and Reissner’s 1944 analysis of the stresses within single lap joints, subsequently extended with the cylindrical stress constraint to tubular lap joints by Lubkin and Reissner in 1956.  Related solutions appear in Spies’ 1953 classic analysis of stresses in peel tests and in Kaeble’s 1960-1965 papers on the stress distributions within pressure sensitive adhesives undergoing peeling.  Most applications of Winkler’s formulation assume that the deflection of adjacent segments are independent, which inherently assumes a Poisson’s ratio of zero for continuous foundations.  When “incompressible” elastomeric foundations are involved, the original 4th order governing ordinary differential equation becomes 6th order, based on the analogous lubrication theory model.  This modified form has become very important for significant advancements in the understanding of stresses and debonding for soft matter adhesion, including both elastomeric solids and hydrodynamic fluid applications.  This presentation is meant as a tribute to Winkler and the significance of his work for the field of mechanics in general, and adhesion science in particular, providing some historical perspective along with some recent extensions to our field.


David Dillard is the Adhesive and Sealant Science Professor in the Biomedical Engineering and Mechanics Department at Virginia Tech. He has worked extensively in the field of adhesive bonding, having experience in structural adhesives for aerospace, automotive, and infrastructure applications; adhesives and coatings for microelectronic applications; pressure sensitive adhesives; elastomeric adhesives and sealants; and polymeric membranes. He has authored or co-authored over 180 refereed publications and regularly teaches courses in adhesion science, polymer viscoelasticity, and sustainable energy solutions. His research involves developing test methods and predictive models for understanding and estimating the performance and durability of polymeric materials, adhesives and bonded joints, using the principles of fracture mechanics and viscoelasticity. Over the past several years he has become active in applying these concepts to sustainable energy products including proton exchange membrane fuel cells and solar photovoltaic applications.  He is a Patrick Fellow and former President of the Adhesion Society and the 2010 recipient of their Award for Excellence in Adhesion Science.  He is the 2013 recipient of the Wake Memorial Medal and an ASME Fellow.  He previously served as Director of the Center for Adhesive and Sealant Science and founded its successor organization, the Macromolecules and Interfaces Institute.