Deformation driven homogenization of fracturing solids

Date

2005-04-01

Author

Birkle, Manuel
Gürses, Ercan
Miehe, Christian

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The paper discusses numerical formulations of the homogenization for solids with discrete crack development. We focus onmulti–phase microstructures of heterogeneous materials, where fracture occurs in the form of debonding mechanisms as wellas matrix cracking. The deﬁnition of overall properties critically depends on the developing discontinuities. To this end, weextend continuous formulations [1] to microstructures with discontinuities [2]. The basic underlying structure is a canonicalvariational formulation in the fully nonlinear range based on incremental energy minimization. We develop algorithms fornumerical homogenization of fracturing solids in a deformation–driven context with non–trivial formulations of boundaryconditions for (i) linear deformation and (ii) uniform tractions. The overall response of composite materials with fracturingmicrostructures are investigated. As a key result, we show the signiﬁcance of the proposed non–trivial formulation of atraction–type boundary condition in the deformation–driven context.

URI

https://hdl.handle.net/11511/87480

DOI

https://doi.org/10.1002/pamm.200510143

Conference Name

76th Annual Meeting of Gesellschaft für Angewandte Mathematik und Mechanik (GAMM), 28 March-01 April 2005

Collections

Department of Aerospace Engineering, Conference / Seminar

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Citation Formats

M. Birkle, E. Gürses, and C. Miehe, “Deformation driven homogenization of fracturing solids,” 2005, vol. 5, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/87480.