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Material point method
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Material point method
The material point method (MPM) is a numerical technique used to simulate the behavior of solids, liquids, gases, and any other continuum material. Especially, it is a robust spatial discretization method for simulating multi-phase (solid-fluid-gas) interactions. In the MPM, a continuum body is described by a number of small Lagrangian elements referred to as 'material points'. These material points are surrounded by a background mesh/grid that is used to calculate terms such as the deformation gradient. Unlike other mesh-based methods like the finite element method, finite volume method or finite difference method, the MPM is not a mesh based method and is instead categorized as a meshless/meshfree or continuum-based particle method, examples of which are smoothed particle hydrodynamics and peridynamics. Despite the presence of a background mesh, the MPM does not encounter the drawbacks of mesh-based methods (high deformation tangling, advection errors etc.) which makes it a promising and powerful tool in computational mechanics.
The MPM was originally proposed, as an extension of a similar method known as FLIP (a further extension of a method called PIC) to computational solid dynamics, in the early 1990 by Professors Deborah L. Sulsky, Zhen Chen and Howard L. Schreyer at University of New Mexico. After this initial development, the MPM has been further developed both in the national labs as well as the University of New Mexico, Oregon State University, University of Utah and more across the US and the world. Recently the number of institutions researching the MPM has been growing with added popularity and awareness coming from various sources such as the MPM's use in the Disney film Frozen.
An MPM simulation consists of the following stages:
(Prior to the time integration phase)
(During the time integration phase - explicit formulation)
The PIC was originally conceived to solve problems in fluid dynamics, and developed by Harlow at Los Alamos National Laboratory in 1957. One of the first PIC codes was the Fluid-Implicit Particle (FLIP) program, which was created by Brackbill in 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. The original MPM was then further extended by Bardenhagen et al.. to include frictional contact, which enabled the simulation of granular flow, and by Nairn to include explicit cracks and crack propagation (known as CRAMP).
Recently, an MPM implementation based on a micro-polar Cosserat continuum 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.
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Material point method
The material point method (MPM) is a numerical technique used to simulate the behavior of solids, liquids, gases, and any other continuum material. Especially, it is a robust spatial discretization method for simulating multi-phase (solid-fluid-gas) interactions. In the MPM, a continuum body is described by a number of small Lagrangian elements referred to as 'material points'. These material points are surrounded by a background mesh/grid that is used to calculate terms such as the deformation gradient. Unlike other mesh-based methods like the finite element method, finite volume method or finite difference method, the MPM is not a mesh based method and is instead categorized as a meshless/meshfree or continuum-based particle method, examples of which are smoothed particle hydrodynamics and peridynamics. Despite the presence of a background mesh, the MPM does not encounter the drawbacks of mesh-based methods (high deformation tangling, advection errors etc.) which makes it a promising and powerful tool in computational mechanics.
The MPM was originally proposed, as an extension of a similar method known as FLIP (a further extension of a method called PIC) to computational solid dynamics, in the early 1990 by Professors Deborah L. Sulsky, Zhen Chen and Howard L. Schreyer at University of New Mexico. After this initial development, the MPM has been further developed both in the national labs as well as the University of New Mexico, Oregon State University, University of Utah and more across the US and the world. Recently the number of institutions researching the MPM has been growing with added popularity and awareness coming from various sources such as the MPM's use in the Disney film Frozen.
An MPM simulation consists of the following stages:
(Prior to the time integration phase)
(During the time integration phase - explicit formulation)
The PIC was originally conceived to solve problems in fluid dynamics, and developed by Harlow at Los Alamos National Laboratory in 1957. One of the first PIC codes was the Fluid-Implicit Particle (FLIP) program, which was created by Brackbill in 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. The original MPM was then further extended by Bardenhagen et al.. to include frictional contact, which enabled the simulation of granular flow, and by Nairn to include explicit cracks and crack propagation (known as CRAMP).
Recently, an MPM implementation based on a micro-polar Cosserat continuum 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.