Modeling of Deformable Tire and Soil Interaction Using Multiplicative Finite Plasticity for Multibody Off-Road Mobility Simulation

Abstract

The objective of this study is to develop a physics-based tire/soil interaction model that can be fully integrated into general multibody dynamics computer algorithms. To this end, a continuum soil model using multiplicative plasticity theory with Drucker-Prager failure criterion is integrated with the high-fidelity flexible tire model developed using the shear deformable laminated composite shell elements for deformable tire/terrain interaction simulation. The element locking of the standard 8-node brick element caused by the tri-linear polynomial can be alleviated by introducing an additional node defining the second derivative of the global position vector at the center of the element, allowing for describing the linear strain distribution over the element volume without introducing enhanced assumed strain (EAS). The benchmark test result indicates that the identical rate of convergence to that of the locking-free 8-node brick element with 9-parameter EAS is obtained using the brick element presented in this study. Since the constitutive equation for soil models is highly nonlinear in nature, involving iterative return mapping algorithm to find the plastic strain every time step, elimination of EAS using the 9-node brick element leads to straightforward implementation for soil model and computationally efficient procedure for tire/soil interaction simulation. Numerical example of deformable tire and terrain interaction simulation is presented to demonstrate the numerical procedure developed in this study.