Parallel Computing of Multi‐scale Finite Element Sheet Forming Analyses Based on Crystallographic Homogenization Method
Since the multi-scale finite element analysis (FEA) requires large computation time, development of the parallel computing technique for the multi-scale analysis is inevitable. A parallel elastic/crystalline viscoplastic FEA code based on a crystallographic homogenization method has been developed using PC cluster. The homogenization scheme is introduced to compute macro-continuum plastic deformations and material properties by considering a poly- crystal texture. Since the dynamic explicit method is applied to this method, the analysis using micro crystal structures computes the homogenized stresses in parallel based on domain partitioning of macro-continuum without solving simultaneous linear equations. The micro-structure is defined by the Scanning Electron Microscope (SEM) and the Electron Back Scan Diffraction (EBSD) measurement based crystal orientations. In order to improve parallel performance of elastoplasticity analysis, which dynamically and partially increases computational costs during the analysis, a dynamic workload balancing technique is introduced to the parallel analysis. The technique, which is an automatic task distribution method, is realized by adaptation of subdomain size for macro-continuum to maintain the computational load balancing among cluster nodes. The analysis code is applied to estimate the polycrystalline sheet metal formability.
Development of Dynamic Explicit Crystallographic Homogenization Finite Element Analysis Code to Assess Sheet Metal Formability
The crystallographic texture evolution induced by plastic deformation in the sheet metal forming process has a great influence on its formability. In the present study, a dynamic explicit finite element (FE) analysis code is newly developed by introducing a crystallographic homogenization method to estimate the polycrystalline sheet metal formability, such as the extreme thinning and “earing.” This code can predict the plastic deformation induced texture evolution at the micro scale and the plastic anisotropy at the macro scale, simultaneously. This multi‐scale analysis can couple the microscopic crystal plasticity inhomogeneous deformation with the macroscopic continuum deformation. In this homogenization process, the stress at the macro scale is defined by the volume average of those of the corresponding microscopic crystal aggregations in satisfying the equation of motion and compatibility condition in the micro scale “unit cell,” where the periodicity of deformation is satisfied. This homogenization a...
Lake Muzahi, Rwanda: limnological features and phytoplankton production
Lake Muhazi, a small lake of Rwanda (East Africa) was studied from 1986 to 1990. A dramatic decrease of the catch of Oreochromis niloticus (350 T y−1 in the fifties vs 30 T y−1 in 1982) suggested a loss of productivity or overfishing. In the same period, other ecological changes occurred: the submerged macrophytes regressed and there was a decrease in Secchi depth (0.65 m in 1987 vs 1.5 m in the fifties). Compared to other lakes of the same area, the plankton production seemed low. The results of the present study characterize lake Muhazi as a shallow lake with a rather unstable diurnal stratification and with slight differences in mixing regime between its eastern, deepest part and its western, shallowest part. Secchi disk depth does not vary seasonally to a large extent. The water has a rather high mineral content (conductivity of about 500 µS cm−1 at 25 °C) and low concentrations of dissolved N and P, except in the hypolimnion, where NHinf4sup+-N can be high.Two species, Microcystis aeruginosa and Ceratium hirundinella, account for most of the phytoplankton biomass, which is about 50–80 mg chlorophyll a m−2 in the euphotic zone, usually with little seasonal variation. Daily gross production estimates amount to about 6 to 9.5 g O2 m−2 d−1 with a significant difference between the two parts of the lake. Data on C:N and C:P ratio in the phytoplankton suggest that some N deficiency might occur in the eastern part. Moreover, the Zm:Zc ratio could also lead to rather low net production rates (0.21–0.25 d−1 for a mixed layer of 4 m)In conclusion, the primary production of lake Muhazi is medium for African lakes and the hypothesis that decreased planktonic production could account for a reduced fish production should be discarded. Whereas the present yield of the fishery is only 20 kg ha−1 y−1, the yield estimated from primary production ranges between 46 and 64 kg ha−1 y−1. This could be reached through proper management. Finally, some hypotheses are given to explain the ecological changes which occurred in the lake.