A basic orthotropic viscoelastic model for composite and wood materials considering available experimental data and time-dependent Poisson’s ratios

Abstract

Long-term deformation in creep is of significant engineering importance. For anisotropic materials, such as wood, composites and reinforced concrete, creep testing in several axial directions including shear is necessary to obtain a creep model which is able to predict deformation in the basic orthotropic case. Such a full set of experimental data is generally not available, and simplifying assumptions are typically made to conceive a useful 3D model. These assumptions should preferably be made based on the material behaviour and sound engineering arguments. This problem appears to be addressed in many different ways and sometimes the assumptions are not well justified. In the present study, we examine 3D creep of wood and composite materials. Particular emphasis is made on explaining the choices made in developing the model, considering practicality, incomplete material data and the specific behaviour of wood and composites. An orthotropic linear viscoelastic model is implemented as a material model in a commercial FE software. The constitutive equations are derived in the 1D case using a hereditary approach, then later generalized to the 3D formulation. Guidelines are shown how to implement it into the FE software to predict creep of components and structures. Although the model itself is conventional, the effect of considering time-dependent Poisson’s ratios is investigated here, as well an optimization approach when inserting inevitably asymmetric experimental creep data into the model. As far as the authors know, creep of wooden materials have not been defined using this approach before. The model of interest is calibrated against experimental data. Examples using experimental results from solid wood data and a unidirectional fiber composite are demonstrated. The results show that the model is able to capture the orthotropic behaviour adequately. Orthotropy requires symmetry of the creep compliance matrix, which typically is not the case experimentally. It is shown that in rendering the matrix symmetric, one needs to decide which direction is more important. It is also shown that the frequently employed assumption of constant Poisson’s ratios should be made with caution.