Random field-based modeling of size effect on the longitudinal tensile strength of clear timber

• Size effect on the longitudinal tensile strength of clear timber.
• Non-Gaussian strength field modeled as 3D random field.
• An upper bound limit for the strength as volume approaches zero.

In the current study, a random field-based size effect model has been proposed for the longitudinal tensile strength of clear timber. Since the failure mode is brittle, the problem is basically an extreme value problem of finding the distribution of minima of strength fields for specimens of different volumes. The stochastic response has been evaluated based on the Monte Carlo method along with the weakest link theory. Within the framework of the spectral representation method, the Weibull distribution has been considered as the marginal distribution to generate realizations of the strength as a 3D random field. The squared exponential autocorrelation function has been used for the description of spatial variability. The error resulting from this model, as compared to existing experimental data in the literature, is much lower than that of the classical Weibull law. The results show that when one of the specimen’s dimensions decreases to less than 10 times the correlation length of the strength field, the size effect starts to deviate from the classical size effect law. Moreover, a simple analytical approximation, which includes the correlation length as length scale, has been presented that facilitates the application of the proposed model.