Implicit finite element formulation of multiresolution continuum theory

The multiresolution continuum theory is a higher order continuum theory where additional kinematic variables account for microstructural inhomogeneities at several distinct length scales. This can be particularly important for localization problems. The strength of this theory is that it can account for details in the microstructure of a material without using an extremely fine mesh. The present paper describes the implementation and verification of a 3D elastic-plastic multiresolution element based on an implicit time stepping algorithm. It is implemented in the general purpose finite element program FEAP. The mesh independency associated with the length scale parameter is examined and the convergence rate of the element is also evaluated.