Relation between the elastic stretchability of stretchable electronics and the cell size of the cellular substrate

With high permeability and low modulus, the cellular substrate can achieve larger elastic stretchability and better wearing comfort than the solid substrate used for stretchable electronics. Since the porosity of the cellular substrate is a dimensionless ratio value, a fixed porosity can result in innumerable cell sizes. And different cell sizes will bring different stiffness, which has a strong impact on the elastic stretchability of stretchable electronics. In this paper, a numerical model is established for a particular structure where the serpentine interconnect is bonded on cellular substrates with the fixed porosity (ϕ=80%). Eight different cell sizes are selected for this porosity and two stretching directions, along and normal to the cell walls, are studied. Base on the results from the model, the curves of elastic stretchability versus the ratio of wall width to serpentine width ratio (δ/w) can be obtained. Results demonstrate that the appropriate ratio δ/w≈1 yields significantly larger elastic stretchability than other cell sizes of cellular substrates. This finding can provide an engineering design regulation for stretchable electronics based on cellular substrates