Abstract
Presented is a rigorous mathematical formulation of boundary value problems defined on discrete systems described by mathematical graphs. The formulation is applicable to mechanical and physical problems and includes an effective algebraic framework and efficient computational implementation. Mechanical problems involving damage initiation and evolution are soled to illustrate the proposed method. It is concluded that the graph-theoretical approach to discrete systems offers substantial benefits in terms of conceptual clarity and computational efficiency.
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Acknowledgments
The author appreciates highly the financial support of EPSRC via grants EP/K016946/1 “Graphene-based Membranes” and EP/N026136/1 “Geometric Mechanics of Solids”.
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Jivkov, A.P. (2019). Analysis of Materials Systems Represented with Graphs. In: Gdoutos, E. (eds) Proceedings of the First International Conference on Theoretical, Applied and Experimental Mechanics. ICTAEM 2018. Structural Integrity, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-91989-8_56
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DOI: https://doi.org/10.1007/978-3-319-91989-8_56
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