Material state remapping in computational solid mechanics

A computational procedure for remapping material state information from one nite element mesh to another is described. The procedure is useful in connection with evolving meshes for inelastic problems, as for example occur in the context of fracture simulation and adaptive mesh re nement. The proposed method is based on weak enforcement of equality between corresponding elds on the two meshes, where piecewise-constant elds on both meshes are generalized from the quadrature-point values. The essential algorithmic problem is that of calculating the volume partition of an arbitrary convex region with respect to a covering set of disjoint convex regions. Instead of geometrically resolving the associated intersections, the problem is herein approximated by a constrained optimization problem, which may be readily and e ciently solved computationally. This formulation is a main contribution of the paper. Computational examples are given that illustrate the e ectiveness of the proposed procedure