Material Point Method
What is Material Point Method?
MPM has evolved from an earlier method developed for fluid dynamics at the Los Alamos National Laboratories, called the particle-in-cell method. MPM consists of moving Lagrangian particles through a Eulerian mesh.
At the end of each calculation cycle, the Eulerian mesh, also referred to as the computational grid, is reset to its original position while the particles remain in their updated position.
Why Material Point Method?
In contrast to traditional FEM, MPM has no need for periodic re-meshing and re-mapping of state variables.
The excessive distortions of an element mesh deforming together with an analysed body lead to inaccuracies in the solution approximation or even to failure of a calculation process due to negative values of Jacobian determinants at points of numerical integration. The use of re-meshing techniques is not a sufficient measure because it is time-consuming and introduces additional errors due to the projection of the solution from a deformed mesh to a regenerated one. Hence, MPM is better suited to model large material deformations. Also, the fact that all the information of the state of the calculation is stored on the particles rather than the mesh, no numerical error results from the mesh returning to its original state after each calculation cycle and no re-meshing algorithm is required.
Furthermore, the particle nature of MPM allows better treatment of crack propagation and other discontinuities compared to traditional FEM. The latter is known to impose mesh orientation on crack propagation in a material. Particle methods are better at handling history-dependent constitutive models.
In comparison to pure particle methods, the calculation of gradients is trivial in MPM as the nodes remain fixed on a regular mesh. Since the particles interact with other particles via the grid, it is very easy to detect contact between entities.
7th MPM Workshop (2013)
6th MPM Workshop (2010)
- A particle method for history dependent materials - Sandia Version
- A particle method for history dependent materials
- An Evaluation of the Material Point Method
- Analysis and Reduction of Quadrature Errors in the Material Point Method
- The Generalized Interpolation Material Point Method
- Improved Velocity Projection for the Material Point Method
- A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations
- Analysis of stress updates in the material-point method
- The material point method in soil mechanics problems
- Application of a particle-in-cell method to solid mechanics
- A weighted least squares particle-in-cell method for solid mechanics
- Tutorial: A beginner’s introduction to the Material Point Method (MPM)
- Enriched Convected Particle Domain Interpolation (CPDI) Method for Analyzing Weak Discontinuities - Page 675
- Finite element method: an introduction
- Fracturing in Concrete via Lattice-Particle Method
- Implicit time integration for the material point method: Quantitative and algorithmic comparisons with the Finite element method
- Implicit dynamics in the material-point method
- Material Point Method Calculations with Explicit Cracks, Fracture Parameters, and Crack Propagation
- Meshfree and Particle Methods and their Applications
- Particle Methods
- Decoupling and balancing of space and time errors in the material point method (MPM)