Plant root penetration and growth as a mechanical inclusion problem

The ability of plant roots to penetrate soils is affected by several stimuli exerted by the surrounding medium, such as mechanical stresses and chemical stimuli. Roots have developed different adaptive responses, such as increase or decrease of the elongation rate of the apical region and swelling or shrinking of its diameter. We propose a mathematical model aimed at explaining the dynamic evolution of plant roots during the penetration into the soil. We treat the root as a cylinder and the root-soil interaction as a purely mechanical inclusion problem. In particular, the root dynamic evolution is based on a modified version of the extended universal law of West, Brown, and Enquist. Coupling the solution of the mechanical problem and the growth equation, we compare the theoretical results with experimental data collected in artificial and real soils. In this work, we propose a plausible interpretation of the experimental results of the root behavior during the growth inside the surrounding soil medium.