[Paper Review] Rheological Model for Wood

Mohammad Masoud Hassani, Falk K. Wittel+2 more|arXiv (Cornell University)|Oct 15, 2014

Rheology and Fluid Dynamics Studies35 references3 citations

TL;DR

This paper presents a 3D orthotropic, moisture-dependent, elasto-plastic and visco-elastic constitutive model for wood, with all material parameters explicitly defined as functions of moisture content. The model is implemented via a UMAT subroutine in FEM, featuring consistent tangent operators for quadratic convergence and validated through numerical simulations and experimental comparisons, demonstrating high accuracy in predicting hygro-mechanical behavior across species including hardwoods and hybrid glulam beams.

ABSTRACT

Wood as the most important natural and renewable building material plays an important role in the construction sector. Nevertheless, its hygroscopic character basically affects all related mechanical properties leading to degradation of material stiffness and strength over the service life. Accordingly, to attain reliable design of the timber structures, the influence of moisture evolution and the role of time- and moisture-dependent behaviors have to be taken into account. For this purpose, in the current study a 3D orthotropic elasto-plastic, visco-elastic, mechano-sorptive constitutive model for wood, with all material constants being defined as a function of moisture content, is presented. The corresponding numerical integration approach, with additive decomposition of the total strain is developed and implemented within the framework of the finite element method (FEM). Moreover to preserve a quadratic rate of asymptotic convergence the consistent tangent operator for the whole model is derived. Functionality and capability of the presented material model are evaluated by performing several numerical verification simulations of wood components under different combinations of mechanical loading and moisture variation. Additionally, the flexibility and universality of the introduced model to predict the mechanical behavior of different species are demonstrated by the analysis of a hybrid wood element. Furthermore, the proposed numerical approach is validated by comparisons of computational evaluations with experimental results.

Motivation & Objective

• To develop a comprehensive, moisture-dependent constitutive model for wood that captures time- and moisture-dependent mechanical behaviors such as creep, plasticity, and mechano-sorption.
• To enable accurate long-term prediction of structural performance in timber components under combined mechanical and climatic loading.
• To provide a robust, numerically stable finite element implementation (UMAT) suitable for use in commercial FEA software.
• To validate the model against experimental data for different wood species, including hybrid configurations like beech-spruce glulam.
• To establish a framework for reliable design of engineered wood structures by accounting for moisture-induced degradation and time-dependent deformation.

Proposed method

• Formulates a 3D orthotropic material model with additive decomposition of total strain into elastic, plastic, visco-elastic, and mechano-sorptive components.
• Defines all material constants (elastic moduli, yield surfaces, creep compliance, mechano-sorption coefficients) as explicit functions of moisture content using experimental data.
• Develops a consistent tangent operator to ensure quadratic convergence in Newton-Raphson iterations during FEM solution.
• Employs a numerical integration scheme based on backward Euler method for time integration of the constitutive equations.
• Incorporates moisture diffusion via Fick’s law with moisture-dependent diffusion coefficients for radial, tangential, and longitudinal directions.
• Validates the model using benchmark simulations and direct comparison with experimental measurements on glued-laminated timber specimens.

Experimental results

Research questions

• RQ1 How can a unified 3D orthotropic constitutive model be developed to capture the full range of moisture- and time-dependent behaviors in wood?
• RQ2 To what extent can the model predict the hygro-mechanical response of different wood species, including hardwoods and hybrid configurations?
• RQ3 How does the inclusion of a consistent tangent operator affect convergence behavior in non-linear FEA simulations of wood?
• RQ4 Can the model accurately reproduce experimental deformations under cyclic drying and mechanical loading?
• RQ5 What is the predictive capability of the model for long-term creep and mechano-sorptive deformation in engineered wood elements?

Key findings

• The model successfully predicts experimental deformations in glued-laminated timber specimens with high accuracy, showing relative errors below 3% for key geometric responses after drying steps.
• Numerical simulations of a hybrid glulam beam made of European beech and Norway spruce demonstrated the model’s flexibility and universality across different species.
• Residual norms in Newton-Raphson iterations dropped below 5×10⁻³ within 3 iterations, confirming robust convergence and stability of the consistent tangent operator.
• The model accurately captures moisture-induced swelling/shrinkage, with hygro-expansion coefficients for beech (radial: 0.00462 /%) and spruce (radial: 0.00330 /%) matching experimental data.
• Creep compliance and mechano-sorptive coefficients were calibrated using time-dependent test data, enabling accurate prediction of long-term deformation under variable moisture and load.
• The FEM implementation via UMAT enabled simulation of complex hygro-mechanical behavior, including stress redistribution and deformation in multi-material wood assemblies.