Size distribution and waiting times for the avalanches of the Cell Network Model of Fracture

The Cell Network Model is a fracture model recently introduced that resembles the microscopical structure and drying process of the parenchymatous tissue of the Bamboo Guadua angustifolia. The model exhibits a power-law distribution of avalanche sizes, with exponent -3.0 when the breaking thresholds are randomly distributed with uniform probability density. Hereby we show that the same exponent also holds when the breaking thresholds obey a broad set of Weibull distributions, and that the humidity decrements between successive avalanches (the equivalent to waiting times for this model) follow in all cases an exponential distribution. Moreover, the fraction of remaining junctures shows an exponential decay in time. In addition, introducing partial breakings and cumulative damages induces a crossover behavior between two power-laws in the avalanche size histograms. This results support the idea that the Cell Network Model may be in the same universality class as the Random Fuse Model

Numerical model of cracking pattern in laminated bamboo specimens under tensile and shear loads

This work describes a two-dimensional numerical model that allows detecting the appearance of cracks and calculating their propagation in elements made of laminated bamboo, under tension and shear. This composite material has long parallel strong cellulose fibers embedded in a weak lignin matrix. The mechanical model that represents the failure and fracture process of laminated bamboo is still unknown. This numerical model simulates localized strains, showing the beginning and progression fracture in the material. The model is based on a two-dimensional scheme for plane stresses, using the finite element method. A one-dimensional plasticity constitutive model, based on Weibull probability distribution, is used to describe the mechanical response of the fibers, and a continuum damage constitutive model controls the behavior of the matrix. The homogenization process is done with the rule-of-mixtures, and vanishing fiber diameter simplification. Continuum strong discontinuities approach is taken as a technique to detect a jump in the displacement field, during the fracture process. This numerical model is used to simulate the failure on tensile and shear tests of laminated bamboo Guadua angustifolia, which were then compared to experimental findings. The results show that the numerical model detects the same crack patterns obtained in tests