Simulating Fractures with Bonded Discrete Element Method

Along with motion and deformation, fracture is a fundamental behaviour for solid materials, playing a critical role in physically-based animation. Many simulation methods including both continuum and discrete approaches have been used by the graphics community to animate fractures for various materials. However, compared with motion and deformation, fracture remains a challenging task for simulation, because the material's geometry, topology and mechanical states all undergo continuous (and sometimes chaotic) changes as fragmentation develops. Recognizing the discontinuous nature of fragmentation, we propose a discrete approach, namely the Bonded Discrete Element Method (BDEM), for fracture simulation. The research of BDEM in engineering has been growing rapidly in recent years, while its potential in graphics has not been explored. We also introduce several novel changes to BDEM to make it more suitable for animation design. Compared with other fracture simulation methods, the BDEM has some attractive benefits, e.g. efficient handling of multiple fractures, simple formulation and implementation, and good scaling consistency. But it also has some critical weaknesses, e.g. high computational cost, which demand further research. A number of examples are presented to demonstrate the pros and cons, which are then highlighted in the conclusion and discussion

Petrography, geochemistry, and geochronology of the Sc-enriched Kiviniemi ferrodiorite intrusion, eastern Finland

The Kiviniemi mafic intrusion, near the eastern margin of the Paleoproterozoic Central Finland Granitoid Complex, is both spatially and temporally associated with post-kinematic Fe-Ti-P-enriched Svecofennian orogenic mafic magmatism. The main rock types in this small (~ 15 ha) intrusion are garnet-bearing fayalite ferrodiorite, leucoferrodiorite, ferromonzodiorite, and pyroxene diorite. The garnet-bearing fayalite ferrodiorite and leucoferrodiorite contain 50-281 ppm Sc, 275-5600 ppm Zr, and 58-189 ppm Y (n = 42), delineating a mineralized deposit some 2.5 ha in extent. Overall, these rocks show an evolved (iron-enriched) tholeiitic character; low values of Ni (<20-40 ppm), Cr (<20 ppm), and Cu (<20-80 ppm); and high contents of Zn (213-700 ppm). The rock-forming minerals in the ferrodioritic rocks are (ferro)hedenbergite, plagioclase (~ An(40)), ferropargasite and ferroedenite, almandine garnet, and fayalite (Fo(1-4)). Accessory minerals include zircon, ilmenite, fluorapatite, biotite, pyrite, pyrrhotite, potassium feldspar, grunerite, and clinoferrosilite. Some relict cumulate textures have been preserved, but primary magmatic features have largely been overprinted by strong recrystallization and corona formation. The main carriers of Sc are amphibole, clinopyroxene, and apatite. The remarkably strong enrichment of Sc in ferromagnesian silicates and apatite, rather than in specific Sc-minerals, implies magmatic enrichment. Post-kinematic mafic intrusions in central Finland constitute a bimodal association with co-existing granitoid counterparts. The Kiviniemi mafic intrusion is associated with a coarse megacrystic granite and the two rock type display mingled contacts, indicative of contemporaneity of the two magmas. This conclusion is in accord with the coincident U-Pb zircon ages for the ferrodiorite, at 1857 +/- 2 Ma (multigrain ID-TIMS) and the megacrystic granite, at 1860 +/- 7 Ma (single-crystal LA-MC-ICP-MS). The initial epsilon Nd value of the ferrodiorite and the granite are + 0.1 and - 2.5, respectively. These Nd isotope compositions probably reflect a chondritic mantle source for the ferrodiorite and suggest incorporation of some Archaean crustal material into the granite in the course of magmatic evolution. The resource estimation calculated for Kiviniemi intrusion by using 40 g/t Sc cut off value is 13.4 Mt of rock with an average grade of 162.7 g/t scandium, 1726 g/t zirconium, and 81 g/t yttrium.Peer reviewe