Application of analysis on graphs to site-bond models of damage evolution in heterogeneous materials

AP Jivkov, TS Todorov, Craig Morrison, Mingzhong Zhang

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    Abstract

    This work demonstrates the use of discrete exterior calculus for efficient solution of lattice models for quasi-brittle media. Applications to the mechanical behaviour of cement pastes and nuclear graphite are shown. Real microstructures are represented by a topologically averaged regular complex of 3D cells. Microstructure details, such size distribution and density of particles and pores, are mapped to the complex to determine geometrical and mechanical properties of cell elements. The complex is reduced to a lattice, the site-bond model, represented as a mathematical graph embedded in 3D. The technology for solving the model with discrete calculus is presented. Porosity effects on the materials elastic properties are analysed to demonstrate agreement with experimental data. Further, the evolution of macroscopic damage is analysed as emerging from the generation and growth of micro-crack population. The results agree very well with measured stress-strain behaviour of the materials. This suggests that the theory can be used for deriving damage evolution as well as cohesive laws for continuum based modelling of fracture in quasi-brittle media.
    Original languageEnglish
    Title of host publicationProceedings of the 11th World Congress on Computational Mechanics
    Place of PublicationBarcelona, Spain
    Pages816
    Publication statusPublished - 20 Jul 2014
    Event11th World Congress on Computational Mechanics - Barcelona, Spain
    Duration: 20 Jul 201425 Jul 2014

    Conference

    Conference11th World Congress on Computational Mechanics
    CityBarcelona, Spain
    Period20/07/1425/07/14

    Keywords

    • Microstructure
    • Lattice-spring model
    • Discrete calculus
    • Micro-cracking

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