The talk is concerned with the modeling and design of objects with unpredictable (unstable) processes. We study a damage propagation in triangular and hexagonal beam lattices and suggest a fault-tolerant design of them. The damage spread is viewed as a quasistatic process, a sequence of breakages of beams followed by an adjustment of the stresses in the remaining structure. It turns out that at each step the stresses in several beams are almost equal which makes the choice of the next failing beam uncertain. We suggest several failure criteria to account for the stress level, imperfections of the beams, and hidden accumulated damage due to prehistory; we also introduce several quantitative parameters for measurements of the damage degree. Simulations of the damage spread using the suggested criteria produce realistic pictures of wiggling and branching cracks. We then discuss principles of robust design of breakable lattices and propose a fault-tolerant design that is an isotropic hybrid between triangular and hexagonal structures.

This is joint work with Michael Ryvkin (Tel Aviv University)