A representative volume element model for the adhesion between a micro-pillared surface and a compliant substrate

A representative volume element (RVE) model was developed to understand how the adhesion response between an effectively rigid substrate with micro-pillar arrays and a compliant substrate is affected by the spacing and aspect ratio of pillars. A number of verification and validation steps were taken to ensure the RVE model was robust. We found that the pull-off force decreases when pillar spacing is small enough such that the local deformation within the compliant substrate around one pillar is affected by neighboring pillars. Additionally, pull-off force can increase dramatically if the compliant substrate makes contact with the back surface between pillars, which occurs when the pillar spacing is large and pillar aspect ratio is small. Our RVE model can provide useful insights and quantitative data for understanding the adhesive contact mechanics between micro-patterned surfaces and soft substrates.