Design of Strain-Limiting Substrate Materials for Stretchable and Flexible Electronics

Abstract

Recently developed classes of electronics for biomedical applications exploit substrates that offer low elastic modulus and high stretchability, to allow intimate, mechanically biocompatible integration with soft biological tissues. A challenge is that such substrates do not generally offer protection of the electronics from high peak strains that can occur upon large-scale deformation, thereby creating a potential for device failure. The results presented here establish a simple route to compliant substrates with strain-limiting mechanics based on approaches that complement those of recently described alternatives. Here, a thin film or mesh of a high modulus material transferred onto a prestrained compliant substrate transforms into wrinkled geometry upon release of the prestrain. The structure formed by this process offers a low elastic modulus at small strain due to the small effective stiffness of the wrinkled film or mesh; it has a high tangent modulus (e.g., >1000 times the elastic modulus) at large strain, as the wrinkles disappear and the film/mesh returns to a flat geometry. This bilinear stress-strain behavior has an extremely sharp transition point, defined by the magnitude of the prestrain. A theoretical model yields analytical expressions for the elastic and tangent moduli and the transition strain of the bilinear stress-strain relation, with quantitative correspondence to finite element analysis and experiments.

Figure 1

Schematic illustrations and optical images of the process for fabricating strain-limiting structures. a,b) Compliant substrate without and with the prestrain. c) Transfer printing a stiff thin film onto the prestrained substrate. d) Releasing the prestrain to form the wrinkled film. e) Stretching the strain-limiting structure. f) Bilinear stress–strain behavior of the strain-limiting structure. g–i) Optical images (scale bar, 1 cm; inset scale bar: 0.5 mm) of the process for applying prestrain to the substrate, transfer printing a stiff thin film on the prestrained substrate, and releasing the prestrain to form the wrinkled film.

Figure 2

Theoretical, numerical, and experimental results from a unidirectional strain–limiting structure. a) Bilinear stress–strain curves of 1 μm-thick PI film on 1 mm-thick Silbione substrate subjected to various prestrains. b) The transition strain versus the prestrain for the PI film on several substrates with thickness ratio H/h = 1000. c) The tangent modulus normalized by the substrate modulus, Ē_tangent/Ē_s, versus the normalized film modulus Ē_f/Ē_s for several thickness ratios H/h. d) The critical film length that separates local wrinkling from global buckling. e,f) Numerical results and optical images (scale bar, 1 mm) of the morphology and out-of-plane displacement for a 1 μm-thick PI film on a 1 mm-thick Silbione substrate subjected to 15.1% prestrain.

Figure 3

a) Schematic illustrations of the fabrication process that uses biaxial stretching. b) Stress-–strain curves for x-, y-, and 45°-stretching of 1 μm-thick PI mesh (width W = 0.1 mm and spacing S = 0.4 mm) on 1 mm-thick Silbione substrate subjected to prestrains of ${\varepsilon }_{\text{pre}}^x=30.8\%$ and ${\varepsilon }_{\text{pre}}^y=15.7\%$. c) The transition strain versus the prestrain for the PI mesh on several substrates with thickness ratio H/h = 1000 and W/S = 1/4. d) The tangent modulus normalized by the substrate modulus, Ē_tangent/Ē_s, versus (W/(W + S)) for PI mesh on several substrates with thickness ratio H/h = 1000. e,f) Numerical results and optical images (scale bar, 200 μm) of morphology and out-of-plane displacement for 1 μm-thick PI mesh (width W = 0.1 mm and spacing S = 0.4 mm) on 1 mm-thick Silbione substrate subjected to prestrains of ${\varepsilon }_{\text{pre}}^x=30.8\%$ and ${\varepsilon }_{\text{pre}}^y=15.7\%$.