Carmeliet, J.1*, Derome, D. 2 and Guyer, R.3


1Chair of Building Physics, ETH Zürich, HIL E 46.3 Wolfgang-Pauli-Strasse 15 CH 8093 Zürich
Empa, Head Lab. for Building technologies, Überlandstrasse 129, CH8600 Dübendorf, Switzerland
jan.carmeliet@empa.ch

2Empa, Swiss Federal Laboratories for Materials Testing and Research ,Wood Laboratory
Überlandstrasse 129, CH8600 Dübendorf, Switzerland
dominique.derome@empa.ch

3University of Massachusetts, USA, Los Alamos National Laboratory, USA

Key words: thermomechanical modeling, wood, moisture coupling, non-linearity elasticity

ABSTRACT

Wood is a cellular material, which shows orthotropy, nonlinear and hysteretic mechanical response and moisture dependent behavior. Experiments show that the dynamic stiffness, when wood is loaded in compression, increases nonlinearly with the stress level (stiffening effect) showing hysteresis upon unloading. The static stiffness is found to decrease linearly with the moisture content up to the fiber saturation point. When increasing the relative humidity, the material adsorbs significantly water, leading to an important swelling of the material, especially in radial and tangential direction. When decreasing again the relative humidity, wood shows a strong hysteresis effect. In conclusion, wood exhibits a strong coupling between moisture and mechanical behavior and behaves fundamentally nonlinearly.

In this paper, we propose a new material model for wood, based on a thermo-mechanical formulation of the change in energy, when a material is mechanically or hygroscopically loaded. The energy formulation includes the mechanical energy of the solid, the energy due to adsorption of the fluid and the energy due to fluid-solid interactions in the porous material. Traditionally, these energies include second order terms in the basic variables, strain and moisture content. The material properties can be obtained by second order differentiation of the energy equation. The material properties include the stiffness, the moisture capacity and a coupling coefficient. In second order energy formulations, the nonlinearity of the material properties has to be determined from experiments.

We present in this paper a higher order formulation of the energy, leading to nonlinear equations for the material properties on strain and moisture content. Advantage of a higher order energy formulation is that the nonlinear dependence of the material properties is inherently taking into account leading to a consistent formulation of the dependence of the material properties on strain and moisture content.

The model is applied to reproduce adequately free swelling due to moisture uptake and strain-stress relations for different moisture contents.