Multifield finite strain plasticity: Theory and numerics

Abstract

Motivated by the inability of classical computational plasticity to fully exploit modern scientific computing, a multifield formulation for finite strain plasticity is presented. This avoids a local integration of the elastoplastic model. In the multifield approach, the balance of linear momentum, the flow relation and the Karush–Kuhn–Tucker constraints are collectively cast in a variational format. In addition to the deformation, both the plastic strain and the consistency parameter are global degrees of freedom in the resulting spatially discrete problem. The ensuing proliferation of global degrees of freedom in the multifield approach is addressed by exploiting the block sparse structure of the algebraic system together with a tailored block matrix solver which can utilise emerging hardware architectures. A series of numerical problems demonstrate the validity, capability and efficiency of the proposed approach.