Constitutive relationship of the fiber cluster of bamboo Guadua angustifolia, determined by means of a Weibull probability function and a model of progressive failure

• We model the mechanical behavior of bamboo G. angustifolia fiber clusters.
• The mechanical properties of individual bamboo fibers should be probabilistic.
• The mechanical behavior of bamboo Guadua angustifolia fiber clusters with a high number of bundles tends to be deterministic.
• The coefficient of variation of the mechanical properties of fiber clusters decreases fast as the number of fiber bundles increases.

Micro-structural analysis shows that the bamboo is a composite material in which the fibers are mainly oriented parallelly to its longitudinal axis. The fibers of a Colombian bamboo called Guadua angustifolia exhibit high tensile strength and elasticity modulus, in spite of the dispersion of its mechanical properties. In this work, a progressive failure model of a fiber cluster with numerous parallel bundles was implemented. In this model the mechanical properties of the fiber bundles follow the same Weibull probability distribution of the experimental results. Numerical simulations show that a cluster with many fiber bundles produce a less disperse mechanical response, even in cases in which independent bundle properties have high dispersion. These results allow observing the fast decrease of the probabilistic scattering of the mechanical properties of the fiber cluster when the number of fiber bundles increases. These results determine the minimum size of a cross section of bamboo G. angustifolia, in order that the fiber cluster has an average mechanical response with a coefficient of variation below a certain value.