Formulations in rates and increments for elastic‐plastic analysis

Abstract

AbstractMinimum principles in velocities, stress rates and plastic strain rates are extended in order to derive formulations for finite increments of displacement, stress and plastic strain fields defining complete numerical methods. Kinematical, statical and mixed principles are developed from a new variational formulation of the elastic‐plastic work‐hardening constitutive relation.The consequences of this time discretization are discussed independently of any discretization of the continuum. In particular, the incremental formulations derived from extended rate principles account for local elastic unloading and produce stress field approximations complying with equilibrium and plastic admissibility without any additional procedure, at least for piecewise linear yield functions. These properties are not fulfilled when the incremental analysis is based on direct discrete versions of classical rate principles.Finally, FEM approximations are formally introduced and the solution of the resulting finite dimensional quadratic optimization problem is considered.