### The discrete element method

iscrete element method (DEM) modeling is a first principle computational method to simulate the behavior of solids, individual particles, and particle aggregates (bulk solids) using physical interaction rules between the discrete elements. Interaction rules that govern inter-particle interactions can include friction, elasticity, cohesion, cementation, viscosity, force at a distance (e.g., gravity, electrostatics), and other physical processes as problem needs require. Solids and particle aggregates are constructed from smaller elements connected by frictional, cohesive, elastic, viscous or cemented bonds that allow objects to deform, erode or fracture under load.

DEM simulations are ideal for granular materials where particles can collide, undergo large, deformation or fail, and for solids that can deform, erode or fail in complex ways. Problem solutions are emergent; meaning that the micro-scale particle interactions produce the global (continuum) scale deformations and forces that are important for engineering design and operations.

Coupi DEM simulates the 3-dimensional properties and processes of granular media and solid materials and their response to external forces and deformations. Granular particles can be represented as spheres, multisphere clusters or polyhedral shapes. Spherical particles are computationally efficient, but do not respond realistically to external loads or deformations. Multisphere clusters are used to represent more complex particles shapes while maintaining the simplicity of spherical contacts. Polyhedral particle shapes are used when realistic shape representation of granular media is required. Particle micro-scale contact algorithms that determine the global-scale constitutive response of granular media are based on physical parameters. Physically realistic simulation models are created by appropriate parameterization of micro-scale properties, such as particle contact friction, elastic moduli, viscosity, surface energy, contact cementation, failure criteria. Engineering designs can be imported from commercial CAD applications or created within Coupi’s software integration environment.