Mechano-chemical Coupling in the Adhesion of
Thin Structures to Surfaces with Topography

Richard M. Springman
Ph.D. Candidate
Advisor: Professor John L. Bassani
Mechanical Engineering and Applied Mechanics
University of Pennsylvania

Abstract

The mechanical and chemical equilibrium fields of adhered cells in both in-vivo and in-vitro microenvironments are coupled through interactions that depend on the local concentrations of certain chemical species (e.g. integrins) and on the local separation of the cell-cell or cell-substrate interface. An adhesive law capturing these dependencies in the presence of mobile species of both strengthening and weakening type is used to study the adhesion of shells to a rigid substrate with surface topography, which is the model system for cell adhesion in 3D micro-environments. The adhesive species, which are confined to the shell surface, are assumed to form an ideal solution with spatially-varying concentrations at equilibrium. Nonlinear shell kinematics accounting for finite rotations of both closed spherical shells and open spherical caps are coupled with the equilibrium equations for axisymmetric deformations and with linearly elastic material response. Changes in the adhesive state under applied load are investigated and pull-off is demonstrated to depend on the chemical fields and loading rate, in addition to the geometry and material properties. Surface topography results in configurations that bridge over low surface features or that conform to the substrate, depending on both the spacing and depth of the features. Equilibrium traction and chemical fields develop patterns that are controlled by the topography. In addition to understanding in-vivo cell adhesion, which almost always involves 3D surface topography, understanding how surface features affect equilibrium is crucial for the engineering of scaffolds used to support cell growth.