A mechanical model for thin sheets

Simulations of thin sheets are a valuable tool for augmenting experimental data sets and revealing the hidden internal dynamics of the sheet’s'deformations. However, it is challenging to develop a model that performs independently of the underlying mesh topology, maps to physical parameters, and scales in a computationally efficient way. Here we employ a mechanical model for a thin sheet based on a general triangular mesh, with linear springs along edges and torsion springs between adjacent triangles. We develop a procedure for locally setting spring constants to match continuum mechanical properties. We test the model's accuracy by running simulations of instabilities in twisted elastic ribbons. We also develop an extension to the model that captures the phenomenology of plastic damage accumulation. Our simulations bridge the gap between image-based experimental data and energy-based theoretical analysis of thin sheet deformations by generating data with fine temporal and spatial resolution.