Anisotropic Mechanics of Cellular Substrate Under Finite Deformation

The use of cellular substrates for stretchable electronics minimizes not only disruptions to the natural diffusive or convective flow of bio-fluids, but also the constraints on the natural motion of the skin. The existing analytic constitutive models for the equivalent medium of the cellular substrate under finite stretching are only applicable for stretching along the cell walls. This paper aims at establishing an analytic constitutive model for the anisotropic equivalent medium of the cellular substrate under finite stretching along any direction. The model gives the nonlinear stress–strain curves of the cellular substrate that agree very well with the finite element analysis (FEA) without any parameter fitting. For the applied strain <10%, the stress–strain curves are the same for different directions of stretching, but their differences become significant as the applied strain increases, displaying the deformation-induced anisotropy. Comparison of the results for linear and nonlinear elastic cell walls clearly suggests that the nonlinear stress–strain curves of the cellular substrate mainly result from the finite rotation of cell walls.