A Statistical Damage Constitutive Model for Wood Along the Grain Direction Based on Poisson Distribution

When constructing a material statistical damage constitutive model based on probability density function, the distribution function determines the accuracy of the constitutive model. The distribution functions used in existing research are primarily applicable to brittle and quasi brittle materials, but not wood. To solve this problem, a Poisson distribution function is introduced, combined with continuous medium mechanics and the geometric conditions of the deformation and failure curve of wood along the grain direction, to construct a statistical damage constitutive timber model along the grain direction. The findings revealed that the method of creating a constitutive model based on the Poisson distribution function proposed in this article was feasible; compared with Weibull distribution, normal distribution, and logarithmic normal distribution, Poisson distribution was more suitable for constructing a wood constitutive model; for the stress-strain curve of the tensile section in the wood constitutive model, a lognormal distribution could also be used to build.