A numerical study of the hygro-mechanical deformation of two cardboard layups

A finite element and a semi-analytical model have been set up to study the hygro-mechanical deformation of two different three-layer square cardboard sheets. Both models are based on a linear constitutive equation and nonlinear von Karman strain–displacement relationships. Results corresponding to steady-state deformations reached after a moisture content change of 5% are presented. Both models agree on the final deformation shapes as well as on the magnitude of the maximal deformation reached. Results show that different equilibrium configurations can be obtained depending on the layer mechanical and expansion properties, the magnitude of the change in ambient conditions, and the inplane dimensions of the cardboard sheet.