Wrinkling evolution of growing fiber-reinforced biological tissues with pre-tension

The instability of film-substrate systems has been studied for decades, but few models have been explicitly linked to skin wrinkling, and the effects of spatial fiber distribution and fiber pretension—critical factors for skin function—are rarely considered. Moreover, the quantitative experimental investigation of the wrinkling evolution in fiber-reinforced biological systems has not yet been conducted, creating a gap between theoretical predictions and real-world applications. In this study, we construct a fiber-reinforced morphoelastic plate model inspired by the skin’s architecture and use linear bifurcation and weakly nonlinear bifurcation analyses to derive analytical predictions for the critical wrinkling onset and wrinkle amplitude. Furthermore, a series of quantitative experiments and finite element simulations are implemented to explore how the fiber distribution and pretension guide the wrinkling onset and subsequent evolution. Notably, both the experimental observations and numerical simulations show remarkable agreement with our theoretical predictions across different conditions. We also examine how various parameters influence the instability characteristics of skin, with particular emphasis on fiber distribution (fibers in the XY, XZ , and YZ planes) and fiber pretension. Our results reveal that fiber distribution in the XY plane combined with the strongest fiber pretension provides the most effective wrinkle resistance. These findings offer mechanistic insight into the stability of skin-like fiber-reinforced layers and provide an experimentally supported modeling framework that can be used to generate systematic datasets for subsequent data-driven studies related to wrinkle formation and, more broadly, tissue remodeling and aging.