Journal
INTERNATIONAL JOURNAL OF DAMAGE MECHANICS
Volume 18, Issue 3, Pages 233-257Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1056789508097544
Keywords
lattice models; microstructure; perturbation analysis; damage parameter; statistical damage mechanics; localization; multiscale models; tensile strength; discrete models
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Funding
- Mathematical, Information and Computational Science Division
- Office of advanced Scientific Computing Research
- U. S. Department of Energy [DE-AC05-00OR22725]
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The article presents a statistical rational model of damage for 2D disordered spring networks under a generic uniaxial loading. The validation is carried out by using the output from numerical simulations of compression and tension tests along the coordinate axes x and y. The findings demonstrate that the rational model works flawlessly in the hardening and softening phases, both for compression and for tension. A clear and intuitive definition of the damage parameter (D) over bar (stated in two alternative forms) is obtained in terms of the combination of three random fields {epsilon(p)*, eta(p), eta p}, which fully encapsulate the complexity of the damage and act as input parameters of the rational model. The analysis of these parameters shed new light on the homogeneous-heterogeneous phase transition of disordered brittle materials and opens up new possibilities in studying and modeling damage processes. The limits of the scalar formulation are also outlined. Simplified models of the rational model are derived and discussed to prove that the apparent complexity of {epsilon(p)*, eta(p), eta p}, npg can be administered by identifying ad hoc simplifying assumptions. The theory is developed for a 2D network but the underlying ideas are general.
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