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A recent result by Gudoshnikov et al [SIAM J. Control Optim. 2022] ensuresfinite-time convergence of the stress-vector of an elastoplastic lattice springmodel under assumption that the vector $g'(t)$ of the applied displacementcontrolled-loading lies strictly inside the normal cone to the associatedpolyhedral set (that depends on mechanical parameters of the springs).Determination of the terminal distribution of stresses has been thereby linkedto a problem of spotting a face on the boundary of the polyhedral set where thenormal cone contains vector $g'(t)$. In this paper the above-mentioned problemof spotting an eligible face is converted into a search for an eligible set ofsprings that have a certain topological property with respect to the entiregraph (of springs). Specifically, we prove that eligible springs are those thatkeep non-zero lengths after their nodes are collapsed with the nodes of thedisplacement-controlled loading after a finite number of eligible displacementsof the nodes of the graph. The proposed result allows to judge about possibledistribution of plastic deformations in elastoplastic lattice spring modelsdirectly from the topology of the associated graph of springs. A benchmarkexample is provided.

Topological properties of elastoplastic lattice spring models that determine terminal distributions of plastic deformations