Topological defects in the buckling of elastic membranes
We investigate the effects of topological defects on the low-energy shapes of single-component two-dimensional elastic membranes with spherical topology. The membrane is described as a closed, triangulated two-dimensional manifold embedded in three-dimensional space using a dynamic triangulation model, thus allowing the creation of topological defects. Low-energy structures and connectivities are explored using a Monte Carlo simulated annealing method while also constraining the internal volume of the membrane to simulate incompressible contents within the membrane, such as in colloidosomes and viruses. We find that since the volume constraint partially suppresses the buckling transition such that the buckled icosahedral shape has a reduced asphericity, defect scars are favorable over a larger range of elastic parameters of the membrane compared with systems having no constraint on volume.