A perturbation force based approach to creasing instability in soft materials under general loading conditions

Abstract

The formation and control of surface creases in soft materials under compression have intrigued the mechanics community for decades and recently found many applications in tissue biomechanics, soft robotics and tunable devices. In spite of a rapidly growing literature in this field, existing methods of analysis often rely on a presumed crease configuration and consequently there is still a lack of profound theoretical understanding on crease nucleation. In this study, we propose a force based perturbation approach to predicting the occurrence of crease nucleation without assuming a post-instability configuration. In a set of carefully controlled FEM simulations, by considering the relative magnitudes among the element size, perturbation displacement and sample size, we find that beyond a critical strain around −0.36, a flat surface under uniform deformation becomes metastable, while the creased configuration becomes stable, with energy barrier for creasing proportional to the square of the FEM element size and therefore vanishing in the continuum limit. Beyond the Biot critical strain of−0.46, the uniformly deformed configuration of a flat surface becomes unstable. Our force-based instability criterion also enabled us to determine the critical conditions of crease formation for different materials under general loading conditions, leading to a set of crease diagrams. Interestingly, it is shown theoretically and validated experimentally that some highly compressible soft materials do not undergo creasing under loading conditions close to equibiaxial compression.