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

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## Abstract

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.

## Keywords

Beam lattice Damage propagation Failure criteria Discrete Fourier transform## Notes

### Acknowledgements

The authors gratefully acknowledge support by DMS, National Science Foundation, Award 1515125 and by Israel Science Foundation, Grant No. 1494/16.

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