Analysis of Materials Systems Represented with Graphs

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.