Mechanics of Secondary Growth

Secondary growth, or the peripheral deposition of load-bearing tissue over time, is not a well-known feature in mechanical engineering. This phenomenon thus requires a careful analysis because inert structures are considered by engineers to exist before being subjected to loading. However, in the case of plants and trees, the structure is already loaded before the new material is laid down, and even during the formation of this new material, mechanical loading continues to occur. For example, when dealing with the local distribution of stresses induced by self-weight in both compression and bending, the solid mechanics theory of homogenous materials would predict a linear distribution from the upper to the lower side. This theory can be modified to take into consideration material heterogeneity within the cross section [35]. In both cases, using formulas from standard mechanical engineering textbooks [8,35] allows us to calculate stresses from the total self-weight and the whole cross-sectional geometry without any data about growth history [7]. However, this analysis implicitly supposes that the total weight has been fixed after the formation of the cross section, whereas in trees, both the weight and cross section grow simultaneously. Taking into account the relative kinetics of cross section and weight growth, Fournier and coworkers [36] emphasized the huge discrepancies when classical engineering theories are used. For example, peripheral wood that is very young supports only a small amount of self-weight, i.e., the weight increment in the above stem and crown since peripheral wood, even when the tree is leaning and self-weight acts as a bending load [37]. This consideration is also of great importance when analyzing successive shapes of growing stems that are continuously bent by gravitational forces (see Section

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