Are Maize Stalks Efficiently Tapered to Withstand Wind Induced Bending Stresses?

Stalk lodging (breaking of agricultural plant stalks prior to harvest) results in millions of dollars in lost revenue each year. Despite a growing body of literature on the topic of stalk lodging, the structural efficiency of maize stalks has not been investigated previously. In this study, we investigate the morphology of mature maize stalks to determine if rind tissues, which are the major load bearing component of corn stalks, are efficiently organized to withstand wind induced bending stresses that cause stalk lodging. 945 fully mature, dried commercial hybrid maize stem specimens (48 hybrids, ∼2 replicates, ∼10 samples per plot) were subjected to: (1) three-point-bending tests to measure their bending strength and (2) rind penetration tests to measure the cross-sectional morphology at each internode. The data were analyzed through an engineering optimization algorithm to determine the structural efficiency of the specimens. Hybrids with higher average bending strengths were found to allocate rind tissue more efficiently than weaker hybrids. However, even strong hybrids were structurally suboptimal. There remains significant room for improving the structural efficiency of maize stalks. Results also indicated that stalks are morphologically organized to resist wind loading that occurs primarily above the ear. Results are applicable to selective breeding and crop management studies seeking to reduce stalk lodging rates. Highlight Maize stem morphology was investigated through an optimization algorithm to determine how efficiently their structural tissues are allocated to withstand wind induced bending stresses that cause stalk lodging.


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Stalk lodging (permanent displacement of plants from their vertical orientation) severely 43 reduces agronomic yields of several vital crop species including maize. Yield losses due to stalk 44 lodging are estimated to range from 5-20% annually (Flint-Garcia et al., 2003;Berry et al., 2007). 45 Several internal and external factors contribute to a plant's propensity to stalk lodge. External 46 factors include wind speed (Wen et al., 2019), pest damage (Echezona, 2007), and disease (Dudley, 47 1994;Holbert et al., 1923). Internal factors include the plant's morphology and material properties 48 (Esechie, 1985;Robertson et al., 2017;Stubbs et al., 2018). Despite a growing body of literature 49 surrounding the topic of maize stalk lodging, a detailed morphological investigation of the taper 50 of maize stalks has not been reported. The purpose of this paper is to quantify changes in diameter 51 and rind thickness of maize stalks as a function of plant height (i.e., taper) and to determine the 52 structural efficiency of the taper of maize stalks. This study investigates stalk taper from a purely 53 structural standpoint and other abiotic and biotic considerations that may affect stalk morphology 54 (i.e., taper) of maize stalks are not considered. 55 To determine the structural efficiency of maize stalks one must both quantify the stalk taper 56 and define probable wind loading scenarios. An efficiently tapered stalk is defined as one in which 57 uniform mechanical stresses are produced when the plant is subjected to probable wind loading 58 scenarios. In other words, the shape of the stalk is optimal, meaning that loads are supported with 59 as little tissue as possible. An inefficient taper is one in which non-uniform mechanical stresses 60 are produced. Inefficient stalks utilize more structural tissue than is necessary in some areas and 61 less structural tissue than is necessary in other areas to withstand the loads to which they are 62 subjected. In other words, for inefficient stalks the amount of structural tissue could be reduced 63 without affecting the load bearing capacity of the stalk. The structural efficiency of maize stalks is 64 of interest because efficient stalks would theoretically have more available biomass and bioenergy 65 to devote to grain filling as compared to inefficient stalks (i.e., efficient stalks would have a higher 66 harvest index).

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As mentioned previously, both the taper and probable wind loading scenarios must be 68 defined to determine the structural efficiency of maize stalks. The wind load exerted on a plant 69 stalk, known as the drag force (Df), can be approximated as (Niklas, 2000): where ⍴ is the density of air, u is the local wind speed, Ap is the projected area of the structure, and 72 CD is the drag coefficient. While this equation appears fairly simple at first glance, it is 73 complicated by the fact that the variables on the right hand side of the equation are functions that 74 can vary both temporally and spatially. For example, the drag coefficient changes spatially along 75 the length of the stalk and is also a function of the local wind speed. As the local wind speed 76 increases, the angle of the leaf blades and tassel change (known as flagging), which alters the drag 77 coefficient.

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The strong interrelationships between the factors of Equation probable wind loading we assume all of the wind force acts at the top of the plant as a point load.

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At the lower bound of probable wind loading we assume a uniform load is applied to stalk along  Figure 1 visually represents each of these assumptions.

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The structural efficiency of maize stalks can be determined by using Engineering equations 113 which relate stem morphology and mechanical stress to probable wind loading scenarios presented 114 in Figure 1. In particular, the maximum stress in any cross-section (σ) due to wind-induced bending 115 is calculated as (Beer et al., 2002): where Df is the drag force (see Equation 1) and Sx is the section modulus at a distance x along the 118 stalk. Section modulus is an engineering term that quantifies the morphology of the cross-

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All maize specimens in this study were subjected to the following battery of tests. and loaded at their middle node. Care was taken to ensure that the specimens were both loaded 181 8 and supported at nodes, and that the span lengths were maximized. This was done to obtain the 182 most natural possible failure modes Stubbs et al., 2018). Specimens were 183 loaded at a rate of 2 mm/s until structural failure. Additional details on the three-point-bending 184 test protocol were documented in a previous study (Robertson et al., 2017  . applied to the top of the specimen as described by Beer (Beer et al., 2002) and shown in Figure   206 2. For the hybrids investigated, the ear was an average of 49.6% (+/-14.3% standard deviation) 207 of the way up the stalk.

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Based on this setup, we can now calculate the resolved force (F0) and the loading profile 209 (f(x)) for each specimen that results in the most uniform stress state in each particular 210 specimen. This was accomplished through the use of an optimization algorithm. In particular, a 211 custom code was developed in Matlab to perform an fmincon optimization for each stem specimen 212 (Chuan et al., 2014;Han, 1977Han, , 1977Sreeraj et al., 2013). The objective of the optimization 213 function was to minimize the variation in mechanical stress across the length of the specimen by with several different initial starting points for each specimen (i.e., initial values for F0 and f(x)) 225 to ensure the global optimal solution was found as opposed to a local minimum. Tolerances and 226 stopping criteria were set to 1E-6 (first order optimality tolerance), 1E-6 (function tolerance), and 227 1E-10 (step size tolerance). Section modulus values for each stalk were analyzed to determine structural efficiency 241 (i.e., how structurally efficient the taper of each stalk was). It was found that the median taper of 242 all stalks demonstrated an efficient allocation of structural tissues for probable wind loadings (see 243 Figure 5). However, many internodes fell well outside the range of structural efficiency (i.e., 244 outside of the white area in Figure 5). In particular, 35% of the measured internodes in the study 245 fell within the most efficient range, 38% of measured internodes fell below the blue curve (too 246 little structural tissue), and 27% of the measured internodes fell above the red curve (too much 247 structural tissue).

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The optimization procedure was performed on all 945 stalks. The fmincon procedure 251 successfully determined the drag force profile (X) that produced the most uniform state for each 252 specimen. Figure 6 depicts histograms of the resulting stress states of the specimens. In particular, 253 the overall average stress along the length of each specimen (n = 945) and the stress at every cross-254 section of each specimen (n = 94500) is presented in Figure 6. To enable all specimens to be 255 plotted on the same graph the stress of each specimen / cross-section was normalized to a target 256 stress of 1.00. In other words, a stress state different than a stress of 1.00 represents a suboptimal 257 allocation of structural tissues.

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Analysis of the drag force profiles for each specimen that would produce the most uniform 259 stress in the specimen revealed that the resolved force F0 was far larger than the drag force profile 260 below the ear (see Figure 7). These data imply that the stalks allocate structural tissues for wind 261 loading that primarily occurs above the ear (e.g. the drag force increases exponentially with 262 height). This does not imply that there is no wind below the ear, but that the drag force (determined

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This was found to be true when comparing individual specimens and when comparing hybrids (see 278 Figure 8). have been developed (e.g., x-ray computed tomography) but these methods are usually limited to 298 laboratory or greenhouse settings and cannot easily be implemented in an agricultural field setting 299 (e.g., (Mairhofer et al., 2012;Robertson et al., 2017;Seegmiller et al., 2020)).

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Results showed that lodging resistant hybrids (i.e., those with higher average bending 301 strengths) were more structurally efficient than hybrids that were weaker. The hybrids with higher 302 average bending strengths also displayed less plant to plant variation in structural efficiency. In 303 other words, strong hybrids were more structurally optimized and more consistently optimized is analyzed as an individual specimen (i.e., no averaging of results across hybrids) the stronger 307 stalks were more structurally efficient than weaker stalks. These results are likely due in part to 308 breeding techniques used in the past. In particular, applied selective breeding pressure based on 309 counts of lodged stalks at harvest time is expected to produce hybrids that are both strong and 310 exhibit minimal plant to plant variance in strength. That is to say that a variety with high average 311 strength but also high standard deviation in strength will have higher lodging rates than a variety 312 with a similar average strength but a lower standard deviation in strength.

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In this study an optimization routine was used to determine the wind loading profile that 314 would produce the most uniform mechanical stresses along the length of maize stalks. It was found 315 that maize stalks are structurally optimized for wind loadings that occur primarily above the (as compared to fluid-structure interaction models) and can infer the aggregate loading over time, 324 taking into account the wind profile and fluid-structure interaction between the wind and the plant 325 stalk.

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Three-point bending tests are the most commonly employed test to quantify bending 327 strength in plant stalks Stubbs et al., 2018). However, results from this 328 study highlight several shortcomings of the three-point-bending test approach. In particular, most 329 plant stalks are tapered and researchers typically opt to place the loading anvil from a three-point- the least optimal allocation of structural tissue). Several devices have been recently developed 342 which accomplish this task (Grafius and Brown, 1954;Berry et al., 2003;Guo et al., 2018Guo et al., , 2019343 Erndwein et al., 2019;Heuschele et al., 2019). In particular, they utilize the natural anchoring of The primary limitation of the current study is that the rind of the stalk was assumed to be 352 a homogeneous, isotropic, linear elastic material subjected to pure bending. The morphology of physiological mature maize stalks was characterized, and the loading 370 environments that result in the most uniform maximum stresses along the length of maize stalk 371 were investigated. It was found that maize stalks are morphologically organized to resist wind 372 loading that occurs primarily above the ear. It was also found that plants with higher bending 373 strengths were more structurally efficient than weaker plants. However, even strong plants