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Root penetration into the soil is essential for plants to access water and nutrients, as well as to mechanically support aboveground structures. This requires a combination of healthy plant growth, adequate soil mechanical properties, and compatible plant–soil interactions. Despite the current knowledge of the static rheology driving the interactions at the root–soil interface, few theoretical approaches have attempted to describe root penetration with dynamic rheology. In this work, we experimentally showed that radish roots in contact with soil of specific density during a specific growth stage fail to penetrate the soil. To explore the mechanism of root penetration into the soil, we constructed a theoretical model to explore the relevant conditions amenable to root entry into the soil. The theory indicates that dimensionless parameters such as root growth anisotropy, static root–soil competition, and dynamic root–soil competition are important for root penetration. The consequent theoretical expectations were supported by finite element analysis, and a potential mechanism of root penetration into the soil is discussed.

This paper addresses a simple energy-based overset finite element method (EbO-FEM) to solve pseudo-static deformation problems consisting of overlapped meshes based on the domain composition method (DCM). This scheme is a non-iterative equation-based method for enforcing the continuity of the displacement field. Hence, the scheme consumes possible minimal computational costs for deformation problems with non-conforming overlapping meshes. The system’s total energy is augmented with continuity constraint energy (CCE) which is a function of the gaps in the displacement field between two overlapping regions. Subsequently, two conventional integration schemes, the Gauss-point projection, and the point-to-point projection, are utilized to discretize the CCE. It is confirmed that both schemes can yield accurate and unique solutions in the overlapped region of the finite element meshes. Further, we proposed a dimensionless relative penalty parameter (DRP). We found that DRP ranging between 1 to 10 is appropriate to robustly obtain accurate solutions for a wide range of scales, stiffness, and geometries, which is supported by three numerical simulations without increasing computational costs after assembling the global matrices and vectors.

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