![]() Because all the material properties are carried by the particles, the solution on the grid at next time step must be reconstructed from the particle information. As a result, no fixed mesh connectivity is required in the MPM so that crack propagation could be simulated without changing the mesh connectivity as needed in the FEM. At the end of each time step, the deformed grid could be discarded to employ a new regular grid in the next time step. The computational mesh of a Lagrangian FEM is attached to the material during the whole solution process, while a specific background grid of the MPM is only attached to the material in each time step. ![]() Therefore, the constitutive equations are evaluated at Gauss quadrature points in the FEM but at particles in the MPM.Ģ. The FEM employs Gauss quadrature to evaluate the integrals in the weak formulation, while the MPM employs particle quadrature. The major differences between the formulations of these two methods are as follows:ġ. Yan Liu, in The Material Point Method, 2017 3.2.4.1 Basic Formulation
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