Stress and strain‐driven algorithmic formulations for finite strain viscoplasticity for hybrid and standard finite elements

Abstract

SUMMARYThis work deals with the formulation and implementation of finite deformation viscoplasticity within the framework of stress-based hybrid finite element methods. Hybrid elements, which are based on a twofield variational formulation, are much less susceptible to locking than conventional displacement-based elements. The conventional return-mapping scheme cannot be used in the context of hybrid stress methods since the stress is known, and the strain and the internal plastic variables have to be recovered using this known stress field. We discuss the formulation and implementation of the consistent tangent tensor, and the return-mapping algorithm within the context of the hybrid method. We demonstrate the efficacy of the algorithm on a wide range of problems.

Stress‐hybrid virtual element method on quadrilateral meshes for compressible and nearly‐incompressible linear elasticity

“…However, very few studies have explored the stress-hybrid method for nonlinear computations. Notable among them are the contributions of Jog and coworkers, [38][39][40][41][42] who have successfully extended the stress-hybrid finite element formulation to nonlinear and inelastic analysis of solid continua, plates and shells.…”