HYSTERETIC MODEL FOR THE EXPLICIT MATERIAL POINT METHOD

Abstract eng:
The material point method (MPM) is an advancement of particle in cell method (PIC), in which Lagrangian bodies are discretized by a number of material points that hold all the properties and the state of the material [1]. All internal variables, stress, strain, velocity etc., that 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. In this work the standard explicit MPM is extended to account for elastoplastic material behavior. The stress-strain constitutive law is determined according to the strain decomposition rule [2] where the strain rates are uncoupled into an elastic and a plastic part. In order to account for the different phases during elastic loading or unloading and yielding two Heaviside type functions are introduced [3]. These act as switches and incorporate the yield function [8]. The final form of the constitutive stress-strain relation incorporates the tangent modulus of elasticity, which now includes the Heaviside functions and gathers all of the governing behavior, facilitating considerably the solution. Numerical results are presented that validate the proposed formulation in the context of the MPM and in comparison with Finite Element Method.

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