For particulate material, continuum level constitutive relations are often not available, especially for those undergoing large and nonequilibrium deformations. One idea is to perform lower-scale simulations to calculate the stresses at the specified locations, such as Gauss points, cell centers and nodes, depending on numerical methods chosen for the continuum level calculation. The lower-scale simulation are often performed in a periodic domains to reduce the effect of the artificial boundaries. For history independent materials, such as ideal gas or low density granular flows, the periodic domain can be Eulerian. For many particulate materials, it is important to keep particle interaction history. For instance, the force chains built up among the granular particles are important for the average stresses in a dense granular material. In such cases, Lagrangian periodic computation domain are required. Unfortunately, for problems with large deformations the computation domain often becomes distorted, and reinitianizations are then needed to continue the calculation. Reinitianizations inevitably lead to the loss all history information.
In this talk, we will introduce a numerical method that keeps the periodic computational domain cuboid, even for very large material deformations, avoiding the need for reinitianization. The method can also accommodate arbitrary velocity gradients. Related numerical steps and physics involved will be explained. Numerical examples will be shown.