A derivation of Griffith functionals from discrete finite-difference models

DOI10.1007/s00526-020-01858-7zbMath1455.49020arXiv2001.00480OpenAlexW3092800249WikidataQ115386985 ScholiaQ115386985MaRDI QIDQ2217798

Vito Crismale, Francesco Solombrino, Giovanni Scilla

Publication date: 14 January 2021

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.00480

zbMATH Keywords

finite-differencesvariational approximationGriffith functionals

Mathematics Subject Classification ID

Brittle fracture (74R10) Methods involving semicontinuity and convergence; relaxation (49J45) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Discrete approximations in optimal control (49M25)

Related Items (7)

From atomistic systems to linearized continuum models for elastic materials with voids ⋮ On some non-local approximation of nonisotropic Griffith-type functionals ⋮ Non-local approximation of the Griffith functional ⋮ Discrete Approximation of the Griffith Functional by Adaptive Finite Elements ⋮ A Γ-convergence result for fluid-filled fracture propagation ⋮ \Gamma-convergence for free-discontinuity problems in linear elasticity: homogenization and relaxation ⋮ Random Finite-Difference Discretizations of the Ambrosio--Tortorelli Functional with Optimal Mesh-Size

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