A particle-in-cell method for solid mechanics

Problems like impact, penetration and large rotations of solid bodies are hard to solve numerically. For these problems, the constitutive equations are history dependent so material points must be followed; this is difficult to implement in an Eulerian scheme. On the other hand, Lagrangian methods typically result in severe mesh distortion, ending in loss of accuracy or efficiency. Remeshing prevents mesh tangling, but mapping history dependent variables to the new grid is error prone. Proposed here is an extension of the particle-in-cell method for solid mechanics. In this method, material points are naturally followed through the complete evolution of the problem. A fixed Eulerian grid provides the means for determining spatial gradients. With the use of maps between the material points and the grid, the advantages of both Eulerian and Lagrangian schemes are utilized and the disadvantages of each are avoided. Examples are presented to illustrate properties of the method. In addition, applications to impact and penetration are discussed.