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The material point method (MPM) is an extension of the particle-in-cell (PIC) method in computational fluid dynamics to computational solid dynamics, and is a finite element method (FEM)-based particle method. It is primarily used for multiphase simulations, because of the ease of detecting contact without inter-penetration. It can also be used as an alternative to dynamic FEM methods to simulate large material deformations, because there is no re-meshing required by the MPM. In the MPM, Lagrangian point masses, or material points, are moved through a Eulerian background mesh. At the end of each calculation cycle, a ‘convective’ step occurs, in which the mesh is reset to its original position, while material points remain in their current positions. There are two key differences between the PIC and MPM. The first one is that the MPM is formulated in the weak form similar to that for the FEM so that the FEM and MPM could be combined together for large-scale simulations. The second one is that history-dependent constitutive models could be formulated on the material points, which results in a robust spatial discretization method for multiphase and multi-physics problems. ==History of PIC/MPM== The PIC was originally conceived to solve problems in fluid dynamics, and developed by Harlow at Los Alamos National Laboratory in 1957.〔Johnson, N.L. "The legacy and future of computational fluid dynamics at Los Alamos". In Proceedings of the 1996 Canadian CFD Conference, 1996〕 One of the first PIC codes was the Fluid-Implicit Particle (FLIP) program, which was created by Brackbill in 1986〔Brackbill, J.U. and Ruppel, H.M. "FLIP: A method for adaptively zoned, particle-in-cell calculations in two dimensions". Journal of Computational Physics, 65, 1986〕 and has been constantly in development ever since. Until the 1990s, the PIC method was used principally in fluid dynamics. Motivated by the need for better simulating penetration problems in solid dynamics, Sulsky, Chen and Schreyer started in 1993 to reformulate the PIC and develop the MPM, with funding from Sandia National Laboratories.〔Sulsky, D., Chen, Z., and Schreyer, H.L. "A particle method for history-dependent materials". Computer Methods in Applied Mechanics and Engineering, 118:179–196, 1994.〕 The original MPM was then further extended by Bardenhagen ''et al.''. to include frictional contact,〔Bardenhagen, S.G., Brackbill, J.U., and Sulsky, D. "Shear deformation in granular materials". 1998〕 which enabled the simulation of granular flow,〔Wieckowski, Z. "A particle-in-cell method in analysis of motion of a granular material in a silo". Computational Mechanics: New trends and Applications, 1998〕 and by Nairn to include explicit cracks〔Nairn, J. A. "Material Point Method Calculations with Explicit Cracks". Computer Modeling in Engineering & Science, 4:649–664, 2003.〕 and crack propagation (known as CRAMP). Recently, an MPM implementation based on a micro-polar Cosserat continuum 〔Coetzee, C.J. The modelling of granular flow using the particle-in-cell method. PhD thesis, University of Stellenbosch, South Africa, 2004.〕 has been used to simulate high-shear granular flow, such as silo discharge. MPM's uses were further extended into Geotechnical engineering with the recent development of a quasi-static, implicit MPM solver which provides numerically stable analyses of large-deformation problems in Soil mechanics.〔Beuth, L., Coetzee, C.J., Bonnier, P. and van den Berg, P. "Formulation and validation of a quasi-static material point method." In 10th International Symposium on Numerical Methods in Geomechanics, 2007.〕 Annual workshops on the use of MPM are held at various locations in the United States. The Fifth MPM Workshop was held at Oregon State University, in Corvallis, OR, on April 2 and 3, 2009. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Material point method」の詳細全文を読む スポンサード リンク
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