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.

细胞在基质上的附着力会对生理行为产生重大影响，并且可能会受到弹性体和生物组织等基质的表面应力，模量和重力作用的影响。在本文中，通过在新霍克超弹性模型的基础上提出结合表面应力和重力效应的预拉伸弹性体的表面格林函数，我们从理论上研究了单元在等双轴预拉伸弹性体上的粘附力。对于在不同的预拉伸，表面应力，表面张力和切向牵引力下的不同无因次重力参数，提出了由单元粘附引起的预拉伸弹性体的表面法向位移。结果表明，先前的参数可能对弹性体基材的表面位移有很大的影响。通常，弹性体的重力和表面应力抑制表面位移，而单元的表面张力和切向牵引力促进弹性体的变形。重力还可以减弱细胞粘附中心的凹形轮廓。此外，预拉伸的增加限制了弹性体基材的表面法向变形。拟议的表面绿色功能在其他领域也有潜在应用，例如压痕，在柔软材料上行走的机器人等。而单元的表面张力和切向牵引力促进了弹性体的变形。重力还可以减弱细胞粘附中心的凹形轮廓。此外，预拉伸的增加限制了弹性体基材的表面法向变形。拟议的表面绿色功能在其他领域也有潜在的应用，例如压痕，机器人在柔软材料上行走等。而单元的表面张力和切向牵引力促进了弹性体的变形。重力还可以减弱细胞粘附中心的凹形轮廓。此外，预拉伸的增加限制了弹性体基材的表面法向变形。拟议的表面绿色功能在其他领域也有潜在的应用，例如压痕，机器人在柔软材料上行走等。