An algorithmic approach to multi-layer wrinkling

Wrinkling, when a thin stiff film adhered to a compliant substrate deforms sinusoidally out of plane due to compression, is a well understood phenomenon in bi-layer systems. However, when there are more than two layers, the wrinkling behavior of the multi-layer system is, at present, not fully understood. In this paper, we provide an analytical solution for wrinkling in tri-layer systems where the additional layers can contribute to either the film stiffness or substrate stiffness. Then, we provide an algorithmic approach for extending our tri-layer analytical solution to systems with multiple additional layers. Our analytical solution and algorithmic approach are verified numerically using the finite element method. Using our methodology, wrinking can be predicted and controlled in multi-layer systems, with applications ranging from stretchable electronics to biomimetic design. In this paper, we demonstrate that our model can be used to understand wrinkling behavior in epidermal electronics.