Biomechanical design of cereal crops steams resistance to lodging: integration of mathematics methods and experimental investigations

Abstract

The paper presents a comprehensive study of the resistance of grain crop stems to lodging using mathematical modeling and experimental analysis. Lodging, which occurs in two forms (root and stem), is a critical factor that reduces crop yields by 30–50% and worsens grain quality. The study focuses on the biomechanical aspects of resistance, considering the stem as a vertical elastic rod of variable cross-section subject to distributed (own weight) and concentrated (ear weight) loads, as well as wind effects. An original mathematical model has been developed based on the differential equations of elasticity theory, including the modified Euler–Bernoulli and Bessel equations for analyzing critical loads. The physicomechanical parameters of stems (elastic modulus, tensile strength) have been experimentally determined for five key crops (wheat, barley, rye, triticale, rice) using the author's bending test technique. It was found that maximum stresses are localized in the middle part of the stem and at the base, which correlates with field observations. The practical significance of the work lies in the creation of tools for predicting lodging risks, optimizing breeding programs (emphasis on short-stemmed genotypes) and agricultural technologies (fertilizer dosing, application of retardants). The need for an interdisciplinary approach combining biomechanics, genetics and precision farming is emphasized. The results show that climatic and agronomic factors affect quantitative, but not qualitative patterns of stability loss, which confirms the universality of the model for different cultivation regions.