Issue 29

N.A. Nodargi et alii, Frattura ed Integrità Strutturale, 29 (2014) 111-127; DOI: 10.3221/IGF-ESIS.29.11 111 Focussed on: Computational Mechanics and Mechanics of Materials in Italy State update algorithm for associative elastic-plastic pressure-insensitive materials by incremental energy minimization N.A. Nodargi, E. Artioli, F. Caselli, P. Bisegna Department of Civil Engineering and Computer Science University of Rome “Tor Vergata”, via del Politecnico 1, 00133 Rome, Italy {nodargi, artioli, caselli, bisegna}@ing.uniroma2.it A BSTRACT . This work presents a new state update algorithm for small-strain associative elastic-plastic constitutive models, treating in a unified manner a wide class of deviatoric yield functions with linear or nonlinear strain-hardening. The algorithm is based on an incremental energy minimization approach, in the framework of generalized standard materials with convex free energy and dissipation potential. An efficient method for the computation of the latter, its gradient and its Hessian is provided, using Haigh-Westergaard stress invariants. Numerical results on a single material point loading history and finite element simulations are reported to prove the effectiveness and the versatility of the method. Its merit turns out to be complementary to the classical return map strategy, because no convergence difficulties arise if the stress is close to high curvature points of the yield surface. K EYWORDS . Plasticity; Hardening; Incremental energy minimization; Dissipation; State update algorithm; Haigh-Westergaard coordinates. I NTRODUCTION he solution of inelastic structural boundary value problems in a typical finite element implementation requires the integration of the material constitutive law at each Gauss point. The complexity of hardening elastic-plastic constitutive equations requires their time discretization and numerical integration on a sequence of finite time steps. This procedure is referred to as the state update algorithm. The most traditional way to formulate the associative plasticity constitutive law is based on the assumption of a convex yield function and the adoption of a normality law to determine the plastic flow. A widely used class of constitutive updates exploiting this framework is the so-called return mapping algorithms. While the basic idea dates back to the work of Wilkins [1], all the return mapping algorithms share the use of an elastic-predictor, plastic-corrector strategy. In particular, in a first step the algorithm checks whether the elastic trial state is plastically admissible. If such is not the case, a solution for the time-discrete plastic evolution equations is sought for in the plastic corrector step. From a geometric standpoint, the return map algorithm amounts to finding the closest point projection, in a suitable norm, of the elastic trial state on the yield domain. To this purpose, a typical method pursued among others in [2-6] consists in the iterative T