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

Peter M Ray,Marion Syndonia Bret-Harte

doi:10.3389/fpls.2019.00059

Peter M Ray, Marion Syndonia Bret-Harte

Open Access

https://doi.org/10.3389/fpls.2019.00059

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Abstract

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.

Highlights

The elasticity of woody-plant branches toward bending under cantilever loads seems obvious, and a number of papers have used bending moduli, measured or inferred for branches, to analyze or predict branches’ behavior under loadings such as by snow (e.g., Schmidt and Pomeroy, 1990), ice, wind (e.g., Sellier and Fourcaud, 2009), or further shoot growth (e.g., Alméras et al, 2002).Woody Branch Viscoelasticitythe viscoelastic aspects of branch bending seem, from the botanical literature, to be largely unappreciated
We have found almost no descriptions of woody branch viscoelasticity in the botanical literature, or elsewhere
The occurrence, in wood, of retarded elasticity was recognized long ago (Kitazawa, 1947; Grossman, 1954; Kollmann, 1961; Kollmann and Coté, 1968). This is relevant to woody branch bending because these structures typically owe their mechanical support mainly to their xylem’s thick secondary cell walls

Summary

Introduction

The elasticity of woody-plant branches toward bending under cantilever loads seems obvious, and a number of papers have used bending moduli, measured or inferred for branches, to analyze or predict branches’ behavior under loadings such as by snow (e.g., Schmidt and Pomeroy, 1990), ice, wind (e.g., Sellier and Fourcaud, 2009), or further shoot growth (e.g., Alméras et al, 2002).Woody Branch Viscoelasticitythe viscoelastic (time-dependent) aspects of branch bending seem, from the botanical literature, to be largely unappreciated. The occurrence, in wood, of retarded elasticity was recognized long ago (Kitazawa, 1947; Grossman, 1954; Kollmann, 1961; Kollmann and Coté, 1968) This is relevant to woody branch bending because these structures typically owe their mechanical support mainly to their xylem’s (wood’s) thick secondary cell walls. In order to characterize the mechanical basis of branch bending, Hogan and Niklas (2004) made bending measurements on strips of linden (Tilia americana) wood. These nicely demonstrated this wood’s viscoelasticity, including both retarded-elastic and irreversible bending, but did not include other features, nor the species breadth, upon which we report here. Several more recent studies model wood cells’ viscoelastic behavior (Engelund and Svensson, 2011; Huc and Svensson, 2018, and refs. there cited)

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