Interactions Between Imposed and Spontaneous Conical Singularities in Surgically Motivated Computational Models

Surgical procedures on channels frequently involve the process of cutting and opening a wedge of material. Medically important in anastomoses and other procedures, this change in geometry is equivalent to imposing an excess cone (e-cone) onto the channel's native curvature and results in stress localization both at and near the intervention site. Such conical structures, as well as developable cones (d-cones) and the resultant ridge structures between these conical singularities, have been widely studied on flat sheets, most often utilizing paper models and theoretical thermodynamic calculations. The impact of additional geometric constraints on the thin sheet, however, is less understood. Motivated by surgical procedures, our work probes the resultant conical structures, ridges, and stress localization associated with imposing e-cones on a cylinder. Utilizing finite element (FE) computational modeling, we first showcase how we can reproduce the geometries of conical structures on flat sheets, validating against theory. We then extend our framework to impose e-cones on a cylinder, characterizing resultant geometries as they relate to various geometric and material properties, such as thickness, cylinder radius, elastic modulus, and multiple imposed conical singularities. Our findings address both a biological and geometric question through computational modeling, building towards our goal of understanding, and ultimately managing, stress localization in surgical contexts.