On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime

DOI10.3934/nhm.2015.10.321zbMath1332.74044arXiv1403.0443OpenAlexW2962749703MaRDI QIDQ258490

Bernd Schmidt, Manuel Friedrich

Publication date: 10 March 2016

Published in: Networks and Heterogeneous Media (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.0443

zbMATH Keywords

brittle materialsfree discontinuity problemsatomistic modelsdiscrete-to-continuum limitsvariational fracture

Mathematics Subject Classification ID

Variational methods for problems in mechanics (70G75) Brittle fracture (74R10) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items (11)

From atomistic systems to linearized continuum models for elastic materials with voids ⋮ A compactness result in \(GSBV^p\) and applications to \(\varGamma \)-convergence for free discontinuity problems ⋮ A continuum model for brittle nanowires derived from an atomistic description by \(\Gamma \)-convergence ⋮ An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem ⋮ Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture ⋮ A derivation of linearized Griffith energies from nonlinear models ⋮ Derivation of Linear Elasticity for a General Class of Atomistic Energies ⋮ A Griffith–Euler–Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanics ⋮ Distribution of cracks in a chain of atoms at low temperature ⋮ Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials ⋮ Asymptotic analysis of microscopic impenetrability constraints for atomistic systems

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