A PARTICLE METHOD FOR HISTORY-DEPENDENT MATERIALS

A broad class of engineering problems including penetration, impact an d large rotations of solid bodies causes severe numerical problems. Fo r these problems, the constitutive equations are history dependent so material points must be followed; this is difficult to implement in a Eulerian scheme. On the other hand, purely Lagrangian methods typicall y result in severe mesh distortion and the consequence is ill conditio ning of the element stiffness matrix leading to mesh lockup or entangl ement. Remeshing prevents the lockup and tangling but then interpolati on must be performed for history dependent variables, a process which can introduce errors. Proposed here is an extension of the particle-in -cell method in which particles are interpreted to be material points that are followed through the complete loading process. A fixed Euleri an grid provides the means for determining a spatial gradient. Because the grid can also be interpreted as an updated Lagrangian frame, the usual convection term in the acceleration associated with Eulerian for mulations does not appear. With the use of maps between material point s and the grid, the advantages of both Eulerian and Lagrangian schemes are utilized so that mesh tangling is avoided while material variable s are tracked through the complete deformation history. Example soluti ons in two dimensions are given to illustrate the robustness of the pr oposed convection algorithm and to show that typical elastic behavior can be reproduced. Also, it is shown that impact with no slip is handl ed without any special algorithm for bodies governed by elasticity and strain hardening plasticity.