Bending of apricot tree branches under the weight of axillary growth: test of a mechanical model with experimental data

Stem orientation is an important factor for fruit tree growth and branching habit since it influences fruit production as well as training practices. A mechanical model of the bending of a stem under axillary load was written and evaluated using experimental data on apricot trees (Prunus armeniaca L.). A set of 15 1-year-old stems of various shapes was observed during the early stage of the growing season when radial growth is still negligible and the loading of the stem increases considerably. The structural modulus of elasticity (MOE) of the stems was estimated through in situ bending tests assuming homogeneous material behaviour. The effect of viscoelasticity was observed through creep tests performed on similar stems during winter. Inputs of the model are initial shape, initial diameter, and final load, defined at various positions along the stem. The final shape was simulated based on different mechanical assumptions, and compared to observations. Assuming small deflections resulted in an underestimate of the mean slope variation of 48%, accounting for large displacements reduced this underestimate to 29% and accounting for viscoelasticity reduced it further to 14%. An adjustment of the structural MOE to fit the final shape led to an excellent fit of the data in most cases, the residual errors for some axes being attributed to material heterogeneity. The use of biomechanical models to predict the shape of fruit trees based on growth parameters, provided adequate assumptions are made, is discussed.