Dual-based adaptive FEM for inelastic problems with standard FE implementations

作者：Widany K U; Mahnken R^*

来源：International Journal for Numerical Methods in Engineering, 2016, 107(2): 127-154.

DOI：10.1002/nme.5156

• finite element
• goal-oriented error estimation
• adaptivity
• dual problem
• inelasticity

Goal-oriented error estimation allows to refine meshes in space and time with respect to arbitrary quantities. The required dual problems that need to be solved usually require weak formulations and the Galerkin method in space and time to be established. Unfortunately, this does not obviously leads to structures of standard finite element implementations for solid mechanics. These are characterized by a combination of variables at nodes (e.g. displacements) and at integration points (e.g. internal variables) and are solved with a two-level Newton method because of local uncoupled and global coupled equations. Therefore, we propose an approach to approximate the dual problem while maintaining these structures. The primal and the dual problems are derived from a multifield formulation. Discretization in time and space with appropriate shape functions and rearrangement yields the desired result. Details on practical implementation as well as applications to elasto-plasticity are given. Numerical examples demonstrate the effectiveness of the procedure.

• 出版日期2016-7-13