Three-dimensional orthotropic nonlinear transient moisture simulation for wood: analysis on the effect of scanning curves and nonlinearity

Abstract

This paper introduces, with the development of user-subroutines in the finite-element software Abaqus FEA®, a new practical analysis tool to simulate transient nonlinear moisture transport in wood. The tool is used to revisit the calibration of moisture simulations prior to the simulation of mechanical behaviour in bending subjected to climate change. Often, this calibration does not receive sufficient attention, since the properties and mechanical behaviour are strongly moisture dependent. The calibration of the moisture transport simulation is made with the average volumetric mass data experimentally obtained on a paired specimen of Norway spruce (Picea abies) with the dimensions $$30\times 15\times 640\, {\mathrm{mm}}^{3}$$ 30 × 15 × 640 mm 3 . The data, from a 90-day period, were measured under a constant temperature of 60 °C and systematic relative humidity cycles between 40 and 80%. A practical method based on analytical expressions was used to incorporate hysteresis and scanning behaviour at the boundary surface. The simulation tool makes the single-Fickian model and Neumann boundary condition readily available and the simulations more flexible to different uses. It also allows for a smoother description of inhomogeneity of material. The analysis from the calibration showed that scanning curves associated with hysteresis cannot be neglected in the simulation. The nonlinearity of the analysis indicated that a coherent set of moisture dependent diffusion and surface emission coefficient is necessary for the correct description of moisture gradients and mass transport.

A three-dimensional numerical analysis of moisture flow in wood and of the wood’s hygro-mechanical and visco-elastic behaviour

“…The Neumann boundary condition that describes the flux that is normal for the exchange surface q n is defined as where s is a moisture-and temperature-dependent surface emission coefficient and w ∞ is the unit-less moisture content of the ambient air. Further information concerning derivation of the FE-formulation and how to iteratively solve the nonlinear system of equations here can be found in Florisson et al (2020) and Johannesson (2019).…”

“…Both analyses used the same geometry and fibre orientation. The moisture flow model was supported by the material routine UMATHT and the boundary condition routine FILM (Florisson et al 2020). The constitutive theory used for the distortion model was implemented in the user-subroutine UMAT.…”

“…5. The input parameters for the moisture flow analysis and its calibration are to be found in Florisson et al (2020). The centre of the beams was located 137.5 mm from the pith, this resulting in a slight curvature of the annual rings in cross section.…”

“…The moisture flow analysis was performed with use of the w -and T-dependent D and s found in Florisson et al (2020). Plots of D r , D t and s are shown in Fig.…”

“…It was shown recently that use of a nonlinear single-Fickian model in connection with nonlinear Neumann boundary conditions is able to describe not only slow MC changes (Konopka et al 2018), but also quick MC changes (Florisson et al 2020). One challenge that brings this model about, is that there is not enough experimental data available to cover the moisture and temperature dependent diffusion coefficient (Avramidis and Siau1987;Rosenkilde 2002) and surface emission coefficient (Yeo et al 2002(Yeo et al , 2008Yeo and Smith 2005).…”