A comparative study of rheology MSD models whose structures are lattice and truss

In this paper, we compare two major structures of MSD (mass-spring-damper) particle models. One is the lattice (hexahedral) structure, and the other is the truss (tetrahedral) structure. They (especially, the truss structure) have been frequently used for representing elastic and/or visco-elastic object. The MSD model efficiently calculates shape deformation of the above materials. In addition, in order to maintain shape precision of each deformation, we carefully calibrate coefficients of damper and spring of Voigt part and a coefficient of damper of the other part in the basic MSD element under many surface points capturing a real rheologic object. A genetic algorithm is used for probabilistic calibration. After the comparison, we get the following properties: (1) the lattice structure has too many elements for calculating force propagation. Therefore, it precisely leads shape deformation with the help of the local (feedforward) volume constant condition. (2) The truss structure does not have enough elements for propagating internal forces, therefore, in order to keep a reasonable volume by expanding its virtual rheology object, we need the global (feedback) volume constant condition. (3) The global condition is time consuming, but can directly control the total volume of virtual rheology object. On the other hand, the local one is quick, but directly expands only a part (voxel) of the virtual object. Therefore, the volume and shape in the lattice structure with the local condition are better than those in the truss structure including the global one. (4) The number of MSD elements in the lattice structure is about two times larger than that in the truss one. Therefore, the former calculation is about two times slower than the latter one. As contrasted with this, the global volume constant condition is strictly two times or slower than the local one. As a result, calculation time of the lattice structure with the local condition is smaller than that of the truss structure with the global one. In conclusion, the lattice structure with the local volume constant condition is the best concerning to calculation cost and shape precision.