The science behind tanuki™

What is the finite element method (FEM)?

The finite element method (FEM) is a computational method widely used to tackle problems in structural analysis, heat transfer and fluid flows. The idea behind the finite-element method is that a complex shape is broken down (discretised) into a finite number of simple shapes (usually triangles when looking at a 2D problem, or tetrahedra in 3D). This allows one to replace the (infinite dimensional) partial differential equations that determine the dynamics for the problem at hand with (finite dimensional) matrix equations. When an analytical solution isn’t available, as is often the case for complex problems in mechanics, FEM allows to calculate quantities such as stresses and deformations with high accuracy.

Scientific reference: Zienkiewicz et al. (2013). The finite element method: its basis and fundamentals. Amsterdam: Elsevier, Butterworth-Heinemann

What about the discrete element method (DEM)?

The discrete element method (DEM) is used to simulate the motion of a large number of discrete particles: for instance by treating granular media as made up of many small spheres and by breaking down time into finite time steps. Because of its simplicity, it is widely used in rock mechanics, powder technology and granular flows. DEM allows to calculate the trajectories and contact forces of particles and to compute both the transient and equilibrium configuration for complex multi-body systems. However, in its standard formulation, is not applicable to problems where individual particles undergo complex deformation.

Scientific reference: Cundall, P.A. and Strack, O.D.L. (1979). A discrete numerical model for granular assembliesGéotechnique, 29(1), pp.47–65

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