A Griffith–Euler–Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanics

DOI10.1142/S0218202517500294zbMath1368.74055arXiv1602.07594OpenAlexW2963863297MaRDI QIDQ4977916

No author found.

Publication date: 17 August 2017

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.07594

zbMATH Keywords

dimension reductiongamma-convergencebrittle materialsthin structuresvariational fractureEuler-Bernoulli beam theoryquantitative piecewise geometric rigidity

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Brittle fracture (74R10) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items (6)

A continuum model for brittle nanowires derived from an atomistic description by \(\Gamma \)-convergence ⋮ A Blake-Zisserman-Kirchhoff theory for plates with soft inclusions ⋮ \Gamma-convergence for free-discontinuity problems in linear elasticity: homogenization and relaxation ⋮ Brittle membranes in finite elasticity ⋮ Two-phase models for elastic membranes with soft inclusions ⋮ A hierarchy of multilayered plate models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime
• Generalised functions of bounded deformation
• An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem
• A derivation of linearized Griffith energies from nonlinear models
• Piecewise rigidity
• The variational approach to fracture
• \(\Gamma \)-convergence for incompressible elastic plates
• Compactness and lower semicontinuity properties in \(SBD(\Omega)\)
• An introduction to \(\Gamma\)-convergence
• Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence.
• Derivation of the nonlinear bending-torsion theory for inextensible rods by \(\Gamma\)-convergence
• The membrane shell model in nonlinear elasticity: A variational asymptotic derivation
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• Revisiting brittle fracture as an energy minimization problem
• An analysis of crystal cleavage in the passage from atomistic models to continuum theory
• Plate theory for stressed heterogeneous multilayers of finite bending energy
• Effective cohesive behavior of layers of interatomic planes
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• Quasistatic evolution of a brittle thin film
• The Föppl-von Kármán equations for plates with incompatible strains
• A Derivation of Continuum Nonlinear Plate Theory from Atomistic Models
• Convergence of Equilibria of Thin Elastic Plates - The Von Karman Case
• Convergence of equilibria of three-dimensional thin elastic beams
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• VI. The phenomena of rupture and flow in solids
• Scaling in fracture mechanics by Bažant law: From finite to linearized elasticity
• Convergence of equilibria for planar thin elastic beams
• Brittle thin films

This page was built for publication: A Griffith–Euler–Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanics