Document Type


Date of Degree

Fall 2016

Degree Name

MS (Master of Science)

Degree In

Mechanical Engineering

First Advisor

Sugiyama, Hiroyuki

First Committee Member

Choi, Kyung K

Second Committee Member

Ratner, Albert


The objective of this study is to integrate a continuum-based deformable tire and terrain interaction model into a general-use physics-based simulation environment capable of off-road vehicle mobility analysis and high-performance computing potential. Specifically, the physics-based deformable tire and terrain models which were recently proposed and validated by Yamashita, et al. will be implemented into the structure of the multi-physics simulation engine Chrono. In off-road vehicle mobility analysis, empirical and analytical models have been commonly used for vehicle-terrain interaction. While these models utilize experimental data or terramechanics theories to create quick predictive mobility models, they are unable to capture the highly nonlinear behavior of soft soil deformation, which can lead to inaccurate or unreliable results. In order to resolve these limitations, the use of physics-based numerical approaches have been proposed. These methods make use of finite element and discrete element simulations to describe the interaction between the vehicle and deformable terrain. Continuum-based finite element models transfer tire forces to the terrain and model the deformation with elasto-plastic constitutive models. Discrete element soil uses a large number of small rigid body particles to describe the microscale behavior of granular terrain, with the deformation of the soil represented by the motion and contact of the particles. While these physics-based models offer a more accurate vehicle-terrain interaction model, the solution procedure can become complex and computationally expensive since co-simulation techniques are often used.

To address these issues, the analysis of physics-based full vehicle dynamics simulations utilizing high-fidelity deformable tire and terrain models in a multi-physics engine with high-performance computing capability is desired. To this end, a continuum mechanics based shear deformable laminated composite shell element proposed by Yamashita, et al. was integrated into the flexible body dynamics simulation framework of Chrono. This element was based on the absolute nodal coordinate formulation and is defined by the global position coordinates and the transverse gradient coordinates of its four nodes. Element lockings are eliminated with the incorporation of the enhanced assumed strain (EAS) and assumed natural strain approaches (ANS). The element formulation includes an extension to model laminated composite materials. Additionally, a locking-free 9-node brick element was integrated into the Chrono framework that makes use of the curvature coordinates at the center of the element. This element is formulated with the Hencky strain measure such that multiplicative finite strain plasticity theory can be used to incorporate soil plasticity models, such as the capped Drucker-Prager failed criterion.

With the shear deformable laminated composite shell element and plastic soil brick element integrated into the Chrono multi-physics simulation engine, an off-road deformable tire and terrain interaction model was developed using the vehicle dynamics simulation module Chrono::Vehicle. An off-road deformable tire model was parameterized based on commercial tire properties and generated as an interchangeable tire model option in the full vehicle dynamics system. Benchmark verification tests were performed to ensure the accuracy of tire deformation and tire force characteristics. Further tests were performed to validate a deformable tire model with a deformable tread pattern constructed from shear deformable shell elements and co-rotational tetrahedral elements. The deformable soil model was also integrated as a terrain option in Chrono::Vehicle and numerical tests were carried out to demonstrate its interaction with rigid and deformable tire models. To make use of the computational performance enhancements available in Chrono, Open Multi-Processing (OpenMP) and Advanced Vector Extensions (AVX) were applied to the evaluation of the elastic force/Jacobian matrix and large matrix operations of flexible bodies, respectively, in order to reduce the computation time by nearly 60%.

Public Abstract

This study aims to develop a physics-based off-road vehicle mobility simulation environment by integrating a deformable tire and terrain interaction model into a multi-physics simulation engine with high-performance computing capability support. Because of the limitations that the empirical and analytical models widely used for vehicle mobility analysis present, there is a need for the development of physics-based mobility simulations that can make use of a single simulation architecture and high-performance computing. In this study, deformable tire and terrain models recently proposed by Yamashita, et al. were integrated into the multi-physics simulation engine Chrono. A structural off-road deformable tire model was designed using a shear deformable laminated composite shell element to model the fiber-reinforced rubber material. Additionally, a continuum-based soil model was integrated into the vehicle dynamics framework of Chrono using the capped Drucker-Prager failure criterion based on multiplicative plasticity theory. These additions allowed for the creation of a high-fidelity full vehicle dynamics simulation that can utilize deformable tires or terrain. Computational performance improvements were made considering Open Multi-Processing and Advance Vector Extensions and additional parallel computing potential exist for future development.


Deformable, Mobility, Simulation, Terrain, Tire, Vehicle


xiii, 85 pages


Includes bibliographical references (pages 83-85).


Copyright © 2016 Bryan Peterson