Elastic and Irreversible Bending of Tree and Shrub Branches Under Cantilever Loads

Tree and shrub branches subjected to cantilever loads such as intercepted snowfall undergo, in addition to the familiar instantaneous elastic bending, a conspicuous retarded-elastic bending, which is commonly 30-50% of their instantaneous bending and occasionally even more. The resultant bending creep that occurs after loading also often includes a slow, time-dependent irreversible bending. These phenomena occur quite generally among woody plants of different major biomes, taxonomic groups, and structural types. We give some of branch bending viscoelasticity's basic physical properties such as load dependence and stress relaxation. These properties belong to the secondary walls of branches' xylem (wood) cells; some properties differ notably from those reported for primary cell walls, a difference for which we propose explanations. A method for separating the overlapping time courses of retarded-elastic and time-dependent irreversible bending shows that multiple retarded-elastic ("Kelvin") elements of branches span a wide range of retardation times (a retardation spectrum, approximate examples of which we calculate), and that irreversible bending can occur in different cases either only in the first few h after loading, or more extensively through 24 h, or (rarely) for several days. A separate time-independent irreversible bending, permanent set, involving a substantial yield stress, also occurs. In three species of shrubs rapid irreversible bending began only several (up to 24) h after loading, implying an unusual kind of viscoelasticity. Deductions from the dynamics of bending suggest that retarded elasticity can help protect branches against breakage by wind gusts during storms. Irreversible bending probably contributes both to the form that tree and shrub crowns develop over the long term, involving progressive increase in the downward curvature and/or inclination of branches, and also to certain other, more specialized, developmental changes.