Physics-based contact using the complementarity approach for discrete element applications in vehicle mobility and terramechanics

• Main Author: Melanz, Daniel J
• Format: Dissertation
• Language: English
• Subjects: computer science; mechanical engineering
• ISBN: 1339740346; 9781339740348

In the context of soil dynamics, terramechanics models fall into three categories of increasing complexity: (i) empirically-based, (ii) continuum-based, or (iii) discrete-based approaches. Empirical methods for modeling wheel performance, like the one used by Wong and Reece, rely on the relationship between soil sinkage and resistance force to infer the normal stress under a wheel. Continuum methods assume matter to be homogeneous and continuous, making it difficult to model soil flow and separation. The discrete element method (DEM) represents soil as a collection of many discrete bodies, or elements, where each element is defined by its size, shape, position, velocity, and orientation. When elements collide, forces and torques are generated using explicit equations.
Despite this wide array of formulations, deformable terrain models that enhance the fidelity of present day vehicle and tire models have been lacking due to the complexity of soil behavior. Purely empirical terrain models are typically only used for "go/no-go" vehicle mobility assessment and have several drawbacks: the parameters can be sensitive to experimental testing procedures, they do not scale well to vehicles with small contact patches, they expose only a small number of model parameters, and they cannot capture 3D effects manifest at the interface between wheel/track and terrain. Continuum-based terramechanics models have been applied with only limited success for general purpose vehicle mobility simulations in off-road conditions since: (a) tire geometry is most often assumed to be simple and described in two-dimensions, which does not capture tread/lug geometry effects on tractive performance, and (b) soil flow effects are also generally ignored or dealt with in an ad-hoc manner. Despite its potential, DEM is currently considered prohibitively expensive due to the amount of data computation that it requires. Recent advances in computer hardware and numerical methods, however, make DEM a viable candidate for real world engineering problems. In particular, solving contact through complementarity requires a small number of model parameters, allows for integration at large step-sizes, and robustly handles the discontinuities in velocities.
This thesis details several enhancements to the complementarity method of contact for discrete element applications in terramechanics. This work is motivated by the degree of fidelity that the discrete element method lends to terramechanics modeling and the advantages that the complementarity formulation provides over alternate contact formulations. Specific enhancements focus on physical modeling and numerical methods, with analytical and experimental techniques used for validation. This basic research is ultimately used to solve a real-world, engineering application, specifically the study of military vehicles operating in off-road terrain conditions.