A statistical damage constitutive model for the uniaxial mechanical behavior of wood based on the Poisson distribution

The constitutive model of materials is fundamental for analyzing the nonlinear behavior of structures. For brittle and quasi-brittle materials, statistical damage constitutive models based on probability density functions offer high computational accuracy. However, existing statistical damage models for wood often show low accuracy, particularly under compressive loading, where discrepancies appear in the softening descending branch of the stress–strain curve. To address this issue, this study proposes establishing a statistical damage constitutive model, takes Yunnan pine and ash wood as examples and proposes a uniaxial statistical damage constitutive model for wood in the longitudinal direction. The model is constructed using the Poisson distribution function, principles of continuum mechanics, and the geometric features of deformation–failure curves. It was implemented as a user-defined material subroutine in the finite element software Abaqus. Numerical simulation results are compared with experimental data to assess the model’s performance. The results indicate that the Poisson distribution-based model can accurately simulate the mechanical behavior of wood, especially under compression and tension. Finite element predictions of stress–strain behavior show strong agreement with test results, with minimal differences in the nonlinear response. This confirms the feasibility and accuracy of applying the Poisson distribution in constitutive modeling of wood.