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Computational model
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Analysis of hygroscopic self-shaping wood at large scale for curved mass timber structures

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Wood bilayers were modeled using the FE method with the above described material model. The geometrical model and BCs are presented in Fig. 4C. The dimensions were chosen according to the experimental sample set described below. The interface region, acting as a diffusion barrier, was modeled by a 0.5-mm-thick and isotropic one-component polyurethane adhesive (1cPUR) by tie connection. The moisture diffusion process (BC for surface moisture flux) was inversely fitted to experimental data of average moisture content evolution over time by comparing the volume-weighted average WMC. Analogy between temperature and moisture was made for modeling transient diffusion using Fick’s second law; ∂ω/∂t = ∇ (D ∇ ω) is equivalent to (ρcT)∂T/∂t = ∇ (KT) when ρcT = 1 so that the matrix of diffusion coefficients D equals the matrix of thermal conductivity coefficients K. In a first step, heat transfer analyses were conducted using 20-node quadratic brick elements. The resulting temperature evolution fields were then used as predefined fields for static analyses with same mesh and elements. A large deformation theory was applied. The resulting bilayer curvature was calculated as $κ=−2uy(uy2+(l+ux2))−1$, using the tip displacements ux and uy and assuming a uniform circle-arc-segment–shaped bilayer of initial length l.

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