Understanding stress focusing in thin solids in the absence of tensile loads

St. Olaf College received a $222,580 Project Grant award from the National Science Foundation's Division of Materials Research (CFDA 47.049 – Mathematical and Physical Sciences) effective October 1, 2025, through July 31, 2026. The award funds fundamental research to develop a predictive framework for understanding stress focusing in thin elastic materials, specifically determining when buckled sheets form sharp, singular features versus smooth configurations. The research employs controlled experiments using polymer films subjected to constrained geometries to measure and quantify stress and strain condensation patterns in the absence of applied tensile loads. The findings are expected to have scale-independent applicability across technologies ranging from graphene films to food packaging to deployable satellites.

The grant incorporates substantive educational and workforce development components that extend beyond core research activities. The project will train two PhD students who mentor undergraduate and high school laboratory participants, and includes a structured outreach program providing six-week summer research internships for high school teachers from Central New York. These educational initiatives align with NSF's commitment to strengthening the Nation's scientific enterprise by building research capacity and broadening participation in the mathematical and physical sciences.

Abstract

Nontechnical abstract thin materials can be bent, twisted, and wrinkled into a multitude of forms. The resulting shapes can be smooth like the undulating edge of a flower, or sharp like the creases and points in a crumpled ball of foil. The goal of this research is to understand when these features turn out to be smooth versus when they are sharp. This deceptively simple question is surprisingly difficult to answer, and IT impacts a variety of technologies that rely on thin sheets. This project consists of a suite of model experiments where polymer films are forced into different geometries, forcing them to buckle. Because the project focuses on physical behaviors that should be scale-free, our discoveries should be applicable to material systems ranging from the very small to the very large, from graphene films to food packaging to deployable satellites. The research is coupled to a set of education and outreach projects that target a wide range of audiences. The project will train two PHD students who will work with undergraduates and high school students in the lab. The work will also engage high school teachers from central new york, who will conduct 6-week summer research internships. Technical abstract despite the ubiquity of sheets in our everyday lives and their importance to a range of technologies, we nevertheless lack a general predictive framework for when a buckled sheet will have a smooth or sharp character. The overarching goal of the project is to measure, quantify, and predict when an elastic film will form sharp, singular features where stresses and strains spontaneously condense to a small set. The project focuses on situations where there are no applied tensile loads to organize the buckling patterns. One set of experiments will use a stamping setup where a thin sheet is confined in the GAP between two curved walls. A second set of experiments will investigate the buckling of an ultrathin spherical cap confined to a liquid bath. The buckling patterns range from smooth concentric circular wrinkles, to smectic domains of parallel wrinkles separated by sharp grain boundaries. The project will characterize the transitions between these morphologies while pursuing a tantalizing link to a polygonalization transition in indented shells. This research lies at the intersections of physics, applied mathematics, and engineering, and the project engages with general themes in condensed matter including singularities, symmetry breaking, and order-disorder transitions. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the foundation's intellectual merit and broader impacts review criteria.- subawards are not planned for this award.