Thermo-mechanical analysis of wood through an asymptotic homogenisation approach

In the last decades the use of wood as a construction material has been steadily increasing. Among the main reasons behind this, are its renewable resource nature and its low environmental footprint. In this context, one of the main challenges faced by engineers during the design process is the knowledge and characterization of wood's thermo-mechanical properties. This is related to the large morphological variations present at the microstructural level, that lead to a wide scatter of the macroscopic properties. To circumvent this issue, in this work a multiscale modelling strategy based on asymptotic homogenisation is proposed. The model is based on the hierarchical nature of wood and incorporates the three material scales generally identified in soft woods: (i) the microfibril scale, (ii) the wood cell scale, and (iii) the growth ring scale. The effective thermomechanical macroscopic properties are obtained by sequentially applying the homogenisation procedure from the microfibril scale all the way up to the macroscopic scale. The model is employed here to investigate the thermo-mechanical response of radiata pine grown in Chile. To determine values of the microstructural parameters that yield macroscopic properties consistent with those observed experimentally, a parameter identification strategy is proposed. The latter considers four elements: an existing experimental database on timber boards density and bending tests, the multiscale model, a timber board bending test finite element model and a genetic algorithm for the optimization procedure. With the resulting microstructural parameters the model is then used to estimate the effective elastic, thermal, and thermo-mechanical properties of radiata pine wood. When compared with measured experimental data and typical experimental values found in the literature, the numerical estimates demonstrate the model predicting capabilities.