Brittle membranes in finite elasticity

DOI10.1002/zamm.202200525arXiv2204.04171OpenAlexW4380048156MaRDI QIDQ6188902

Stefano Almi, Dario Reggiani, Francesco Solombrino

Publication date: 8 February 2024

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.04171

zbMATH Keywords

diffeomorphismrecovery sequencelocal immersionfractured configurationmaximal-rank subgradient constraintvariational reduced model

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Brittle fracture (74R10) Energy minimization in equilibrium problems in solid mechanics (74G65) Membranes (74K15) PDEs in connection with mechanics of deformable solids (35Q74)

Cites Work

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• Derivation of a homogenized nonlinear plate theory from 3d elasticity
• Effective behavior of nematic elastomer membranes
• Reduced models for linearly elastic thin films allowing for fracture, debonding or delamination
• Hemihelical local minimizers in prestrained elastic bi-strips
• The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells
• Derivation of von Kármán plate theory in the framework of three-dimensional viscoelasticity
• The nonlinear membrane energy: variational derivation under the constraint ``\(\det \nabla u\neq 0\)
• A variational model for fracture and debonding of thin films under in-plane loadings
• The nonlinear membrane energy: Variational derivation under the constraint ``det\(\nabla u>\)0
• The variational approach to fracture
• \(\Gamma \)-convergence for incompressible elastic plates
• An introduction to \(\Gamma\)-convergence
• Construction of nonsingular isoperimetric films
• Derivation of the nonlinear bending-torsion theory for inextensible rods by \(\Gamma\)-convergence
• A global method for relaxation in \(W^{1,p}\) and in SBV\(_p\)
• Quasistatic evolution of perfectly plastic shallow shells: a rigorous variational derivation
• A nonlinear model for inextensible rods as a low energy \(\varGamma\)-limit of three-dimensional nonlinear elasticity
• The membrane shell model in nonlinear elasticity: A variational asymptotic derivation
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons
• On the approximation of SBV functions
• Homogenization of free discontinuity problems
• On global and local minimizers of prestrained thin elastic rods
• \(\Gamma\)-convergence of free-discontinuity problems
• A quasistatic evolution model for perfectly plastic plates derived by \(\varGamma\)-convergence
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• Quasistatic evolution of a brittle thin film
• MODELING OF A MEMBRANE FOR NONLINEARLY ELASTIC INCOMPRESSIBLE MATERIALS VIA GAMMA-CONVERGENCE
• Optimal design and relaxation of variational problems, III
• Partial Differential Relations
• A density result in SBV with respect to non-isotropic energies
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• Thin-walled beams with a cross-section of arbitrary geometry: Derivation of linear theories starting from 3D nonlinear elasticity
• Relaxation of singular functionals defined on Sobolev spaces
• A Griffith–Euler–Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanics
• A dimension-reduction model for brittle fractures on thin shells with mesh adaptivity
• Derivation of Elastic Theories for Thin Sheets and the Constraint of Incompressibility
• Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity
• Linearized plastic plate models asΓ-limits of 3D finite elastoplasticity
• Brittle fracture in linearly elastic plates
• Direct methods in the calculus of variations

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