Dorian L. Linero

A statistical model of fracture for a 2D hexagonal mesh: The Cell Network Model of Fracture for the bamboo Guadua angustifolia

Abstract A 2D, hexagonal in geometry, statistical model of fracture is proposed. The model is based on the drying fracture process of the bamboo Guadua angustifolia . A network of flexible cells are joined by brittle junctures of fixed Young moduli that break at a certain thresholds in tensile force. The system is solved by means of the Finite Element Method (FEM). The distribution of avalanche breakings exhibits a power law with exponent − 2.93 ( 9 ) , in agreement with the random fuse model (Bhattacharyya and Chakrabarti, 2006) [1] .

Variation in the Fiber Percentage in Specimens of Laminated Bamboo Guadua angustifolia

Raw bamboo is a composite graded naturally material with variable distribution of fibers in the culm wall thickness and also in height. The strength and fiber volume fraction obtained in tests of round bamboo are very variable, while laminated bamboo has more uniform properties. The fiber volume fraction was determined in two groups of specimens of laminated bamboo Guadua angustifolia and also in two groups of bamboo clapboards. Although the average values of fiber volume fraction was around 45% for all cases, it was found that the coefficient of variation in the groups of specimens of laminated bamboo guadua was 6%, while in the groups of slats was 29%.

Determination of Shear Stress in Pull out Tests in Laminated Bamboo Guadua angustifolia

Specimens of laminated bamboo Guadua angustifolia do not usually fail due to fiber breakage when submitted to shear stresses. The common failure mechanism in that case is slippage in the fiber-matrix interface, accompanied by degradation of the lignin matrix (parenchyma). In this study the shear strength of laminated bamboo Guadua angustifolia specimens was determined by tension tests reducing the cross section area. The perimeter of the slipped area was determined using digital image processing. Shear stresses were calculated taking into account the load and slipped area in specimens of two different groups, depending on the orientation of the laminated boards. It was found that the average value of the shear strength on pull out tests were 2.9 MPa, which is a mechanical property of the material that is useful, for example, in the analysis of the behavior of the joints, and analysis of the fracture process.

The Elastic Modulus and Poisson's Ratio of Laminated Bamboo Guadua angustifolia

Laminated bamboo is a natural composite material with cellulose fibers, parenchyma cells, and vascular bundles. The mechanical characterization of this material includes not only the determination of its strength, but also of its elastic constants. Given the anisotropic nature of the laminated material, compression tests were performed on three groups of specimens. The elastic modulus in the load direction and the Poissons ratio were determined, and the results showed that the materials physical anisotropy causes an anisotropic mechanical behavior. The average values obtained for the elastic modulus ranged from 30044 MPa for group 1 to 265 MPa for group 2. The results of the test to determine the Poissons ratio in compression perpendicular to the fibers, ranged from 0.013 to 0.278 whereas those obtained in compression parallel to the fibers, ranged from 0.621 to 1.506.

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

Abstract 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 histogram of avalanche sizes. This results support the idea that the Cell Network Model may be in the same universality class as the Random Fuse Model.