Wood properties and especially wood density have been used as functional traits organized along major axes of species life history and strategy. Beyond statistical analyses, a better mechanistic understanding of relationships among wood traits is essential for ecologically relevant interpretation of wood trait variations. A set of theoretical relationships mechanistically linking wood basic density with some other wood traits is derived from cellular material physics. These theoretical models picture basic physical constraints and thus provide null hypotheses for further ecological studies. Analysis is applied to data from two original datasets and several datasets extracted from the literature. Results emphasize the strong physical constraint behind the link between basic density and maximal storable water on the one hand, and elastic modulus on the other hand. Beyond these basic physical constraints, the developed framework reveals physically less expected trends: the amount of free water available for physiological needs increases in less dense wood of fast-growing species, and the cell wall stiffness decreases with density in temperate hardwoods and is higher in sapling stages in the rainforest understorey where competition for light is associated with high mechanical risk. We emphasize the use of theoretically independent traits derived from models of cellular material physics to investigate the functional variation of wood traits together with their environmental and phylogenetic variations. Although the current study is limited to basic density, green wood lumen saturation and wood specific modulus, we further emphasize the identification of complementary independent wood traits representing other biomechanical functions, nutrient storage, hydraulic conductance and resistance to drought.