The material point method (MPM) is an advancement of particle in cell method, in which Lagrangian bodies are discretized by a number of material points that hold all the properties and the state of the material. All internal variables, stress, strain, velocity, etc., which specify the current state, and are required to advance the solution, are stored in the material points. A background grid is employed to solve the governing equations by interpolating the material point data to the grid. The derived momentum conservation equations are solved at the grid nodes and information is transferred back to the material points and the background grid is reset, ready to handle the next iteration. In this work, the standard explicit MPM is extended to account for smooth elastoplastic material behavior with mixed isotropic and kinematic hardening and stiffness and strength degradation. The strains are decomposed into an elastic and an inelastic part according to the strain decomposition rule. To account for the different phases during elastic loading or unloading and smoothening the transition from the elastic to inelastic regime, two Heaviside-type functions are introduced. These act as switches and incorporate the yield function and the hardening laws to control the whole
Computational Particle Mechanics – Springer Journals
Published: May 28, 2018
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