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This research examines a Discrete Element Method (DEM) for modeling the behavior of sand under various loading conditions as a critical first step in developing computational tools to aid in designing new sand-tire interaction systems for improved traction and mobility. Sand as a material is challenging to model computationally due to its unusual behavior: sometimes resembling a fluid and sometimes behaving more like a solid, yet never exactly replicating either. This behavior arises from the particulate nature of sand which, in contrast to the systems typically modeled in continuum mechanics, is not readily represented by continuum models. In sand, elements (i.e. particles) do not have permanent associations with neighboring elements as they do in most continua, but rather are free to migrate anywhere in the domain according to their interactions with other elements.

To facilitate the design of a non-pneumatic tire for NASA's new Moon mission, the authors used the Finite Element Method (FEM) to investigate the interaction between soil and non-pneumatic tire made of different cellular shear bands. Cellular shear bands, made of an aluminum alloy (AL7075-T6), are designed to have the same effective shear modulus of 6.5E+6 Pa, which is the shear modulus of an elastomer. The Lebanon sand of New Hampshire is used in the model. This sand has a complete set of material properties in the literature and Drucker-Prager/Cap plasticity constitutive law with hardening is employed to model the sand. The tires are treated as deformable bodies, and the authors used the penalty contact algorithm to model the tangential behavior of the contact. The friction between tire and sand is considered by using Coulomb's law. Numerical results show deformation of sand and tire.