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. Author manuscript; available in PMC: 2018 Jan 5.
Published in final edited form as: Adv Funct Mater. 2016 Nov 2;27(1):1604281. doi: 10.1002/adfm.201604281

Figure 2. Modeling studies of the influence of various parameters on spatial distributions of strain in engineered substrates.

Figure 2

(a) Schematic illustration of engineered substrates with uni-directional variations in thickness. (b) Effect of geometric nonlinearity on strain distributions in a ‘step’ substrate at four different uniaxial levels of strain (left), effect of thickness ratios (5, 10 and 20) on strain distributions in ‘linear transition’ substrates at 15% applied strain (middle), and effect of substrate geometries (step, sloped step, linear, convex parabolic, and concave parabolic) on distributions of strain distributions at 15% applied (overall) strain (right). Side views of the corresponding engineered substrates in their unstrained states appear at the bottom bottom. (c) Inverse design results for linear (left) and parabolic (middle) distributions of strain enabled by optimized variations in thickness, with fitted lines shown in black dashes for comparison, and thickness as a function of position for each inverse design (right).