An effective strategy observed in nature for resisting external destructive forces is to avoid
localized catastrophic failure by damage of distributed sacrificial elements. This phenomenon
significantly contributes to the remarkable mechanical properties of many biological materials.
By absorbing energy under extreme loading conditions, these materials can undergo substantial
deformations while remaining intact. A specific composite material microstructure can achieve
this effect by incorporating distributed weak bonds that fail first. They are found, for example,
in the organic adhesive holding together nacre tablets and in bone collagen tissue. Beyond
bimaterial composites, the sought microstructure can also be generated by the specific shape
voids in solid parent material. The periodic two-dimensional architected lattice cellular materi-
als that realize this opportunity are the subject of the present communication. Their controlled
quasi-static brittle failure behavior is considered by modeling the microstructure as a network
of Euler-Bernoulli beam elements (links) rigidly connected at the nodal points [1-3].

For the study of the damage propagation dynamics, the model with massless links and
point masses at the nodal points is applied. The problems of impulse and step-function load-
ings applied to the straight linear lattice boundary are considered. As a result of the failure of
periodically located separated sacrificial links, the initial lattice material tranforms to a new
one with reduced stiffness, and the phase transition takes place. Two waves types are observed:
sacrificial elements failure wave and leading elastic wave propagating in front of it in the un-
damaged lattice. Consequently, the elastic wave velocity exceeds that of the damage front.
Due to the breakage of sacrificial elements, the internal force's amplitude in the leading wave
is significantly lower than the applied force's magnitude. The high frequency vibrations caused
by the breakage of sacrificial elements are localized within the damaged layer and do not affect
the leading wave. In practice, the vibration energy finally goes to heat due to the non-linearity
of a natural parent material. It is found that the increase of the applied force raises both the
damage wave velocity and the leading wave amplitude. However, the amplitude variation is
notable only for small applied force values near the fracture initiation limit. The thickness of
the partly damaged material layer can far exceed that of the fully damaged layer in lattice
materials of the same relative density, which lack a specific architecture with sacrificial bonds.
Therefore, for the optimal parameters combination, the sacrificial bonds layout can not only
preserve the specimen shape after unloading but also provide outstanding energy absorption
properties.

References:
[1] Cherkaev, A and Ryvkin, M. Damage propagation in 2D beam lattices: 2. Design of an
isotropic fault-tolerant lattice, Archive of Applied Mechanics , 89, 503-519, 2019.
[2] Ryvkin, M., Slesarenko, V., Cherkaev, A., Rudykh, S. (2019). Fault-tolerant elastic-
plastic lattice material. Philosophical Transactions of the Royal Society, Series A, 378, Article
20190107.
[3] Bolshak, G. and Ryvkin, M. Bio-inspired beam lattice materials with sacrificial bonds.
International Journal of Engineering Science 193 (2023) 103938.