Numerical homogenization of the Eshelby tensor at small strains

DOI10.1177/1081286517724607zbMath1482.74147OpenAlexW2753397495MaRDI QIDQ5133819

Dietmar Gross, Ralf Mueller, Charlotte Kuhn, Markus Klassen

Publication date: 11 November 2020

Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/1081286517724607

zbMATH Keywords

finite element methodrepresentative volume elementnumerical homogenizationconfigurational forcemacroscopic Eshelby tensor

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Homogenization in equilibrium problems of solid mechanics (74Q05)

Cites Work

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• A computational framework of configurational-force-driven brittle fracture based on incremental energy minimization
• A comparison of different approaches in the multi-scale computation of configurational forces
• A computational framework of three-dimensional configurational-force-driven brittle crack propagation
• On material forces and finite element discretizations
• A multiscale approach for modeling progressive damage of composite materials using fast Fourier transforms
• An introduction to computational micromechanics.
• Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy.
• Configurational forces and their application in solid mechanics
• Application of material forces to hyperelastostatic fracture mechanics. I: Continuum mechanical setting
• Use of material forces in adaptive finite element methods
• A numerical method for computing the overall response of nonlinear composites with complex microstructure
• The nature of configurational forces
• Effective properties of composite materials with periodic microstructure: A computational approach
• Configuration forces as basic concepts of continuum physics
• Configurational Forces
• The determination of the elastic field of an ellipsoidal inclusion, and related problems
• A robust algorithm for configurational-force-driven brittle crack propagation with R-adaptive mesh alignment
• [https://portal.mardi4nfdi.de/wiki/Publication:3899665 Einige Erhaltungss�tze der Kontinuumsmechanik vom J-Integral-Typ]
• On configurational forces in the context of the finite element method
• Mechanics in Material Space
• Fracture Mechanics
• On constitutive macro-variables for heterogeneous solids at finite strain
• The force on an elastic singularity
• An approach to micro-macro modeling of heterogeneous materials
• Application of material forces to hyperelastostatic fracture mechanics. II: Computational setting.

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