Configurational–Force–Based Adaptive Methods in Nonlocal Gradient‐Type Inelastic Solids

Abstract

AbstractWe propose a configurational‐force‐based framework for h‐adaptive finite element discretizations of solids with nonlocal, gradient‐type constitutive response. Typical applications are related to gradient‐type damage mechanics, strain gradient plasticity and regularized brittle fracture. On the theoretical side, we outline a general incremental variational framework for the multifield problem of gradient‐type dissipative solids, where generalized internal variable fields account for the current state of evolving microstructures. The Euler equations of the multifield variational principle define the macroscopic balance of momentum along with balance‐type evolution equations for the generalized internal variables in the physical space as well as the balance of configurational forces in the material space. We propose a staggered computational scheme for satisfying those balances in both the physical as well as the material space. The coupled micro‐ and macro‐structural balances of momentum and internal variables provide a solution in the physical space for a given finite element mesh. The balance in the material space is then used to provide an indicator for the quality of the finite element mesh and accounts for a subsequent h‐type mesh refinement. Such a configurational‐force‐based approach provides in a natural and unified format mesh refinement indicators for a broad class of complex nonlocal problems. This framework is applied to damage‐type regularized brittle fracture. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)