Finite element simulation of stress relaxation process in living cells

In this manuscript, we investigated the fundamental mechanism of stress relaxation phenomenon by employing finite element simulation. Through finite element simulations, the evolution of stress distribution, deformation field and the interaction force was wholly recorded during both the loading and stress relaxation stages. With the developed simulation model, the sensitivity of force-time curves on cell height and substrate stiffness was thoroughly studied by changing the thickness of cell and Young's modulus of the substrate. The simulation results indicated that the variation of cell height leads to the significant change of F-t curve's magnitude but tiny deviation of the curve's shape. And the influence originates from the substrate can be totally eliminated with relatively hard substrate. Finally, using the viscoelastic parameters extracted from actual stress relaxation experiment, the dynamic mechanical behavior of L929 cells is simulated and investigated. A comparison between the experimental and simulation F-t curves demonstrated the effectiveness of the proposed finite element simulation approach