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Two‐scale diffusion–deformation coupling model for material deterioration involving micro‐crack propagation
Author(s) -
Terada Kenjiro,
Kurumatani Mao
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2835
Subject(s) - homogenization (climate) , nonlinear system , brittleness , deformation (meteorology) , scalar (mathematics) , materials science , mechanics , cracking , scale (ratio) , coupling (piping) , scalar field , statistical physics , classical mechanics , physics , mathematics , composite material , geometry , biodiversity , ecology , quantum mechanics , biology
Abstract In this paper, we introduce a two‐scale diffusion–deformation coupled model that represents the aging material deterioration of two‐phase materials involving micro‐crack propagations. The mathematical homogenization method is applied to relate the micro‐ and macroscopic field variables, and a weak coupling solution method is employed to solve the two‐way coupling phenomena between the diffusion of scalar fields and the deformation of quasi‐brittle solids. The macroscopic mechanical behavior represented by the derived two‐scale two‐way coupled model reveals material nonlinearity due to micro‐scale cracking induced by the scalar‐field‐induced deformation, which can be simulated by the finite cover method. After verifying the fundamental validity of the proposed model and the analysis method, we perform a simple numerical example to demonstrate their ability to predict aging material deterioration. Copyright © 2010 John Wiley & Sons, Ltd.