Simulating Self-Avoiding Isometric Plate Bending

DOI10.1137/21M1440001zbMath1490.74003arXiv2108.04952MaRDI QIDQ5084516

Sören Bartels, Frank Meyer, Christian Palus

Publication date: 24 June 2022

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.04952

zbMATH Keywords

plate bendingnonlinear elasticityself-avoidancetangent-point energyinjective isometriesdiscrete Kirchhoff triangles

Mathematics Subject Classification ID

Plates (74K20) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids (74-10)

Uses Software

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• ParaView
• ALUGrid
• DUNE-ALUGrid

Cites Work

• Tangent-point repulsive potentials for a class of non-smooth \(m\)-dimensional sets in \(\mathbb R^n\). I: smoothing and self-avoidance effects
• A generic grid interface for parallel and adaptive scientific computing. I: Abstract framework
• A generic grid interface for parallel and adaptive scientific computing. II: Implementation and tests in DUNE
• Injectivity and self-contact in nonlinear elasticity
• Global curvature and self-contact of nonlinearly elastic curves and rods
• Rigorous derivation of nonlinear plate theory and geometric rigidity
• Modeling and simulation of thermally actuated bilayer plates
• Self-interactions of strands and sheets
• Discontinuous Galerkin approach to large bending deformation of a bilayer plate with isometry constraint
• Variations of deformations with self-contact on Lipschitz domains
• Plate theory for stressed heterogeneous multilayers of finite bending energy
• On rectifiable curves with \(L^{p}\)-bounds on global curvature: self-avoidance, regularity, and minimizing knots
• Minimal energy configurations of strained multi-layers
• Injectivity and self-contact in second-gradient nonlinear elasticity
• Approximating \(W^{2,2}\) isometric immersions
• Global curvature for surfaces and area minimization under a thickness constraint
• Projection-free approximation of geometrically constrained partial differential equations
• THE ENERGY SPACES OF THE TANGENT POINT ENERGIES
• Bilayer Plates: Model Reduction, Γ-Convergent Finite Element Approximation, and Discrete Gradient Flow
• Global curvature, thickness, and the ideal shapes of knots
• A simple scheme for the approximation of self-avoiding inextensible curves
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• Approximation of Large Bending Isometries with Discrete Kirchhoff Triangles
• Stability of a simple scheme for the approximation of elastic knots and self-avoiding inextensible curves
• Stable gradient flow discretizations for simulating bilayer plate bending with isometry and obstacle constraints
• DG approach to large bending plate deformations with isometry constraint
• Introduction
• Finite Elements

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