Finite element analysis of crack problems for strain gradient material model

A strain gradient material model is developed within the framework of infinitesimal deformation theory and implemented using a finite element simulation. Discussing the governing equations involving the second gradient terms, a complete form of the strain gradient material model is derived. The gene...

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Published in:Philosophical magazine (Abingdon, England) England), 2005-11, Vol.85 (33-35), p.4245-4256
Main Authors: Imatani, S., Hatada, K., Maugin, G. A.
Format: Article
Language:English
Subjects:
Condensed matter: structure, mechanical and thermal properties
Deformation and plasticity (including yield, ductility, and superplasticity)
Exact sciences and technology
Fatigue, brittleness, fracture, and cracks
Mechanical and acoustical properties of condensed matter
Mechanical properties of solids
Physics
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description A strain gradient material model is developed within the framework of infinitesimal deformation theory and implemented using a finite element simulation. Discussing the governing equations involving the second gradient terms, a complete form of the strain gradient material model is derived. The generalized variational principle, the so-called 'Hu-Washizu principle', is applied to the mixed-type finite element stiffness equation, in which the displacement, the strain, and the second gradient of displacement are variants. The stress-strain concentration is examined, and emphasis is placed on the explicit scale dependence of the objective domain. Stress relaxation behaviour near the crack tip is, in general, observed for small cracks, and the energy release rate calculated through the conventional J-integral is no longer path-independent for such scale-dependent crack problems.
doi_str_mv 10.1080/14786430500363544
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subjects Condensed matter: structure, mechanical and thermal properties
Deformation and plasticity (including yield, ductility, and superplasticity)
Exact sciences and technology
Fatigue, brittleness, fracture, and cracks
Mechanical and acoustical properties of condensed matter
Mechanical properties of solids
Physics
title Finite element analysis of crack problems for strain gradient material model
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