Mechanical and Chemical Effects in Adhesion of Thin Shell Structures with Applications in Wafer Bonding and Adhesion of Living Cells

A theoretical model is analyzed to investigate the adhesion of thin shell structures to both rigid and deformable substrates under a variety of surface conditions. The thermodynamic forces driving the adhesive process are determined from an interfacial free energy, which is described within a classical thermodynamics framework. Deformations of the thin, elastic shells are studied using a geometrically nonlinear shell theory. Finite-range adhesive tractions, chemical segregation, substrate compliance, and substrate topography all are considered over a wide range of geometric and material parameters. Equilibrium adhesion states are characterized by a shell flatness parameter, the contact radius, and the adhesive and elastic energies. The nonlinear, coupled differential equations governing mechanical and chemical equilibrium are studied using finite differences and numerical continuation methods. The analysis has applications in wafer bonding and the adhesion of living cells.