A two‐scale generalized finite element approach for modeling localized thermoplasticity

Predicting localized, nonlinear, thermoplastic behavior and residual stresses and deformations in structures subjected to intense heating is a prevalent challenge in a range of modern engineering applications. The authors present a generalized finite element method targeted at this class of problems, involving the solution of intrinsically parallelizable local boundary value problems to capture localized, time‐dependent thermo‐elasto‐plastic behavior, which is embedded in the coarse, structural‐scale approximation via enrichment functions. The method accommodates approximation spaces that evolve in between time or load steps while maintaining a fixed global mesh, which avoids the need to map solutions and state variables on changing meshes typical of traditional adaptive approaches. Representative three‐dimensional examples exhibiting localized, transient, nonlinear thermal and thermomechanical effects are presented to demonstrate the advantages of the method with respect to available approaches, especially in terms of its flexibility and potential for realistic future applications in this area. Parallelism of the approach is also discussed. Copyright © 2016 John Wiley & Sons, Ltd.