Modeling and simulation of thin sheet folding
Sören Bartels, Andrea Bonito, Péter Hornung
2022Interfaces and Free Boundaries Mathematical Analysis Computation and Applications12 citationsDOIOpen Access PDF
Abstract
The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling conditions on the energy and the geometric properties of the folding arc in dependence on the small sheet thickness. The resulting two-dimensional model is a piecewise nonlinear Kirchhoff plate bending model with a continuity condition at the folding arc. A discontinuous Galerkin method and an iterative scheme are devised for the accurate numerical approximation of large deformations.
Topics & Concepts
PiecewiseHyperelastic materialFolding (DSP implementation)Nonlinear systemArc (geometry)Arc lengthScalingBendingGalerkin methodMathematicsGeometryMathematical analysisStructural engineeringPhysicsEngineeringQuantum mechanicsAdvanced Numerical Methods in Computational MathematicsElasticity and Material ModelingContact Mechanics and Variational Inequalities