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Deformation Driven Homogenization of Fracturing Solids
Author(s) -
Gürses Ercan,
Birkle Manuel,
Miehe Christian
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510143
Subject(s) - homogenization (climate) , classification of discontinuities , materials science , mechanics , nonlinear system , smoothing , discretization , microstructure , deformation (meteorology) , boundary value problem , cracking , computer science , mathematics , mathematical analysis , physics , composite material , biodiversity , ecology , quantum mechanics , computer vision , biology
The paper discusses numerical formulations of the homogenization for solids with discrete crack development. We focus on multi–phase microstructures of heterogeneous materials, where fracture occurs in the form of debonding mechanisms as well as matrix cracking. The definition of overall properties critically depends on the developing discontinuities. To this end, we extend continuous formulations [1] to microstructures with discontinuities [2]. The basic underlying structure is a canonical variational formulation in the fully nonlinear range based on incremental energy minimization. We develop algorithms for numerical homogenization of fracturing solids in a deformation–driven context with non–trivial formulations of boundary conditions for (i) linear deformation and (ii) uniform tractions. The overall response of composite materials with fracturing microstructures are investigated. As a key result, we show the significance of the proposed non–trivial formulation of a traction–type boundary condition in the deformation–driven context. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)