Damage propagation in 2d beam lattices: 1. Uncertainty and assumptions

Andrej Cherkaev*, Michael Ryvkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


The paper studies damage propagation in brittle elastic beam lattices, using the quasistatic approach. The lattice is subjected to a remote tensile loading; the beams in the lattice are bent and stretched. An introduced initial flaw in a stressed lattice causes an overstress of neighboring beams. When one of the overstressed beams fails, it is eliminated from the lattice; then, the process repeats. When several beams are overstressed, one has to choose which beam to eliminate. The paper studies and compares damage propagation under various criteria of the elimination of the overstressed beams. These criteria account for the stress level, randomness of beams properties, and decay of strength due to micro-damage accumulation during the loading history. A numerical study is performed using discrete Fourier transform approach. We compare damage patterns in triangular stretch-dominated and hexagonal bending-dominated lattices. We discuss quantitative characterization of the damage pattern for different criteria. We find that the randomness in the beam stiffness increases fault tolerance, and we outline conditions restricting the most dangerous straight linear crack-like pattern.

Original languageEnglish
Pages (from-to)485-501
Number of pages17
JournalArchive of Applied Mechanics
Issue number3
StatePublished - 15 Mar 2019


FundersFunder number
National Science Foundation1515125
Division of Mathematical Sciences
Israel Science Foundation1494/16


    • Beam lattice
    • Damage propagation
    • Discrete Fourier transform
    • Failure criteria


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