## 4 Discussion
### Mechanics and Dynamics  
A stress strain curve can be applied to plant stems. As seen in Figure 7, the positive linear relationship between stress and strain of a material is known as [PERSON]'s modulus (\(\gamma\)). The yield strength is where the curve becomes non-linear, and the stress begins to relax slightly as the strain increases. Stretching occurs between the yield and ultimate strengths of the material, where the material is taking the most stress that it is physically capable. Stretching then occurs during the elongation (and relaxation) phase, as the material yields even further, breaking bit by bit on the microstructurallevel, before its eventual ultimate failure, when a mechanical separation of the material into two or more pieces occurs. Living tissues have a property unique in nature in that they can regenerate their structures and place themselves back in the linear region of the stress strain curve after yield has occurred if active growth of the organism is occurring [20]. In the case of a stem that is being stretched, it elongates as a force bends it past its bend radius, causing the junctions between the cell walls in the outer side of that bend to yield. This separation results in stem snap in plants such as corn and barley [21; 22; 23; 24], and can cause the release of roots from the substrate (i.e., soil) resulting in root lodging in oats and other plants [1]. For the purposes of this paper, the measurements of ultimate material failure and root lodging are not discussed. Stem strength is defined as being proportional to the amount of force needed to push the stem over to a given angle. The strength of a material can be described in several ways. In the most common definition is yield strength, the amount of force under which the structural integrity of a material begins to fail. There is also the interpretation of strength as the difference between different parts of the stress-strain curve, i.e., when a material begins to deform at a different rate, along with ultimate strength, the maximum stress the material can bear even after deformation. The force on a material in tension is usually denoted as being divided by its cross-sectional area, resulting in the formula:  
\[\sigma=\ \frac{F}{A}\]  
where \(F\) is the force exerted in Newtons, \(A\) is the cross-sectional area in m\({}^{2}\), and \(\sigma\) the stress in Pascals. The extension or elongation of the material is then calculated as its strain (\(\epsilon\)), a dimensionless number often expressed as a percentage:  
\[\epsilon=\ \frac{l}{l_{\text{initial}}}\]  
Figure 7: Anatomy of a typical stress-strain curve. The text in red indicates movement for a biomaterial, such as the stem or roots of a grass. where \(l\) is the current length of the material, \(l_{initial}\) is the initial length of the material and is the strain on the material. Thus, the characterization of a material as with a linear relationship between stress and strain (the Young's modulus, \(\gamma\)) is only true when the material's stress has not yet transited its yield strength. The elasticity of the stem is determined by its Young's modulus and yield strength. The elasticity is the property of the stem's strain to remain linear over a wide range of applied forces. Elasticity confers resistance to lodging by allowing for recovery of the stem to close to its initial position, once the force that was acting upon the stem ceases. Thus, smaller septum size [25], and conical stem [23; 26] profiles expressed by most cereals would hypothetically confer the most resistance to lodging on a given stem. Therefore, in the case of oat lodging resistance, the difference in displacement measured (\(p=0.0016\)) may suggest a difference of overall stem form and septum size. This lack of recovery to the original starting position in lodging susceptible oat cultivars may also suggest a lack of elasticity in the stems or may even be evidence of micro-structural failures within the stem compared to resistant cultivars.