## 1 Introduction  
Lodging is a complex trait in which both external and internal forces contribute to overall change in plant structural integrity. Plants respond by either bending with the force or remaining rigid. A stem that is too rigid is at risk of becoming unanchored from the substrate via root slippage (root lodging) or buckling somewhere along the stem (stem lodging). Both types of lodging in small grain cereals can decrease yield [1] and grain quality [2] resulting in large economic losses to producers and processors [3]. Plant breeders currently screen for lodging resistance using a visual rating scale to quantify the degree to which lodging occurs after weather events with strong winds. One limitation of this method is that weather events with wind speeds that are either too low or too high will not reveal phenotypic variation for lodging among breeding lines and therefore limit the selection that can be imposed by the breeder [1]. Since weather events are stochastic in nature, for years researchers have been attemptingto use physical mechanics to describe and quantify lodging in cereal grains independent of weather events. Multiple methods have been developed to quantify bending and stem strength in plants. [PERSON] and [PERSON] [4], developed a method that relied on attaching a load (i.e., chains) to the tip of an oat inflorescence and measuring the curvature of the stem (cLr). Stems that had a greater curvature were correlated with lodging resistance [4]. This method was laborious and thus abandoned for a quicker in situ method called snap score where an individual applied pressure to stems using an arm or stick and then visually rated the amount of immediate recovery with a score value [5]. Although the variance of snap score is similar to the cLr [5], the precision is variable from person to person and practice is required for mastery of the technique. As the field of electronics advanced, in situ pull force [6] and push force meters [7] to measure stalk strength were developed and improved [8; 9]. Pull force meters [6] assume stem deformation to be a Hookean spring phenomenon in one dimension. By assuming that the stem behaves as a Hookean spring (i.e., F = -kx applies to it) this model, ignores the nature of tissue deformation in a plant. Additionally, pull force meters specialize in single stem testing and are more likely to damage plants in situ, which makes this tool more suited for measuring stem failure in larger cereal plants such as maize or sorghum. Push force meters differ by measuring the average the force of a group of stems making these instruments ideal for small cereal grains such as wheat, rice and oats. However, the comparison of these measurements requires similar seeding densities between samples. Push force meters use a pivot approach [7; 9]; modeling stem strength in this way accounts for tissue deformation in a non-linear elastic phenomenon of two dimensions. The pivot model assumes that motion is rotationally symmetric around the axis of growth; however this type of motion may not be true in all cases because prevailing winds may act to strengthen the growth of the stem in anisotropic ways [10]. This type of modeling, similar to the pull force meters, does not take into account the elasticity of the stem along its length, the conical form of the stem across its height, or the cLr [4]. Both current designs of push and pull force meters allow for quantification of stem strength which has been associated with lodging resistance [6; 8; 11]. Unfortunately, measuring just stem strength does not take into account elasticity, the ability of the stem to return from deformation in more than one dimension, which plays a role in a stem's ability to recover from wind gusts [4; 12; 13]. Although the estimation of lodging heritability is improved when using stalk strength compared to the traditional rating scale [7; 11], it is clear that the complexity of lodging cannot be explained by stalk strength alone.