Adhesion of a cell on a prestretched elastomer incorporating gravity effect

Abstract

The adhesion of a cell on the substrate can play a significant effect on the physiological behavior, and may be affected by the surface stress, the modulus and the gravity effect of the substrate like elastomers and biological tissues. In this paper, by proposing a surface Green function of a prestretched elastomer incorporating the surface stress and the gravitational effect on the basis of the neo-Hookean hyperelastic model, we have theoretically studied the adhesion of a cell on the equi-biaxially prestretched elastomer. The surface normal displacement of the prestretched elastomer resulted from the adhesion of a cell is presented for different dimensionless gravity parameters at different prestretches, surface stresses, surface tensions and tangential tractions. The results show that the previous parameters can have a large impact on the surface displacement of the elastomeric substrate. Generally, the gravity and the surface stress of the elastomer suppress the surface displacement, while the surface tension and the tangential traction of the cell promote the deformation of the elastomer. Gravity can also attenuate the concave profile of the adhesion center of a cell. Furthermore, the increase of the prestretches restrains the surface normal deformation of the elastomer substrate. The proposed surface Green function has also potential applications in other fields, such as indentation, robot walking on soft materials, etc.