Simple model for compression of cellular materials exhibiting serial buckling of the microstructure

Cellular materials are ubiquitous in nature systems and a variety of engineering fields. Although structural disorder in the cellular material plays an important role for the mechanical property, it is not well studied from the view point of physics. This study proposes a simple compression beam grid model of a cellular material as a minimal model for discussing the role of disorder. The model is composed of beams, which exhibit buckling at random strain, and a buckling chain reaction occurs probabilistically due to concentrated stress, which affects the stress-strain curve. The contribution of the model's parameters on the probability of serial buckling are estimated under weak disorder condition and under some approximations. Validity of the analysis is confirmed by numerical simulations.