Application of the Finite Element Method in Agricultural Soil Mechanics

Abstract

The Finite Element Method (FEM) is a powerful numerical technique that can be used to analyze complex engineering problems. It is particularly useful for problems that include geometric and/or material nonlinearities, as well as situations where underlying differential equations describing physical or biological phenomenon are nonlinear. Since most soil-machine/soil-plant interaction problems involve both material and geometric nonlinearties, FEM has been widely used to analyze soil/machine and soil/plant interaction problems. For example, in a root growth or a tillage problem interface elements are necessary to properly model the soil-root or soil-tillage tool interface. Moreover, soil is an elasto-plastic material that leads to material nonlinearity. A soil-traction device (a tire, for example) interaction problem involves geometric nonlinearity due to the soil-tire interaction (contact problem) and the elasto-plastic behavior of soil as well as the tire material (a layered, composite, incompressible material). Furthermore, these problems include large displacements and strains. The availability of many commercial general purpose software packages such as ANSYS and ABAQUS, which incorporate elasto-plastic behavior of soil and include a large selection of element types including contact and interface elements, makes FEM a particularly attractive technique to analyze soil-machine interaction problems. However, it should be noted that intrinsic to the use of FEM in the context of soil-machine interaction is the assumption that continuum mechanics applies to this case<footnote> Alternate methods that do not require continuum assumptions, such as the Discrete Element Method (DEM), have been used in soil mechanics with some success. Their primary disadvantage is the requirement of huge computer memory even to solve a very small problem, since equations of motion of each particle within the system and its interaction with its neighbor are continuously accounted. There is a potential to reduce computational costs while still taking advantage of the capabilities of DEM to model fracture by combining FEM and DEM methods (Mujiza et al, 1995). The original formulations of DEM were derived for purely frictional materials and have been applied for analyzing the behavior of sands. Anandarajah (1994) extended the DEM model to include cohesive behavior of soils. Initial research towards simulating the behavior of adhesive and cohesive-frictional agricultural soils in soil-tire and soil-tool interaction problems using DEM were reported by Oida et al. (1999) and Tanaka et al. (1999), respectively.