Issue 29

N.A. Nodargi et alii, Frattura ed Integrità Strutturale, 29 (2014) 111-127; DOI: 10.3221/IGF-ESIS.29.11 121 finite element mesh is constituted by 24×24 OPT-DKT triangular elements (see [38, 42], for instance). The analysis is conducted under displacement control, up to a total displacement of 300 c.u., coinciding with the cylinder radius. Fig. 4(b) depicts the deformed configuration at the final load level, while in Fig. 4(c) load-displacement diagram is plotted. The numerical solution appears to be in good agreement with the reference one [39]. The slight difference at high displacement values may be attributed to different finite-element types used in the computations. CONCLUSIONS new state update algorithm for small-strain associative elastic-plastic constitutive models was presented. It is set within the theoretical framework of generalized standard materials with internal variables, under the assumption of rate independence. The evolution of internal variables in a finite time step obeys an incremental minimization principle involving a suitable convex functional, given by the sum of internal energy and dissipation function. An efficient strategy to compute the latter and its gradient and Hessian is proposed, using Haigh-Westergaard stress invariants, for an ample class of isotropic deviatoric yield functions with linear or nonlinear strain-hardening. Numerical results proved the effectiveness and the versatility of the methodology on a single material point state update, for a given loading history under mixed stress/strain control, and showed its reliability as an efficient constitutive solver in conjunction with finite element simulations. The proposed algorithm turned out to be complementary to the classical return mapping strategy, because no convergence difficulties arise if the stress is close to points of the yield surface with high curvature. Hence it may improve the robustness of available plastic solvers through a hybrid approach. Future work will involve the modeling of pressure-sensitive yield surfaces and non-associative plastic flow rules, and the testing of the solution algorithm on extensive large-scale FE simulations of engineering-relevant problems. ACKNOWLEDGMENT he financial support of PRIN 2010-11, project “Advanced mechanical modeling of new materials and technologies for the solution of 2020 European challenges” CUP n. F11J12000210001 is gratefully acknowledged. R EFERENCES [1] Wilkins, M.L., Calculation of elastic-plastic flow, Methods of Computational Physics, Academic Press, New York, 3 (1964). [2] Simo, J.C., Taylor, R.L., Consistent tangent operators for rate-independent elastoplasticity, Comput. Meth. Appl. Mech. Eng., 48 (1985) 101–118. [3] Simo, J.C., Taylor, R.L., A return mapping algorithm for plane stress elastoplasticity, Int. J. Numer. Methods Eng., 22 (1986) 649–670. [4] Ortiz, M., Popov, E.P., Accuracy and stability of integration algorithms for elastoplastic constitutive relations, Int. J. Numer. Methods Eng., 21 (1985) 1561–1576. [5] Ortiz, M., Simo, J.C., An analysis of a new class of integration algorithm for elastoplastic constitutive relations, Int. J. Numer. Methods Eng., 23 (1986) 353–366. [6] Ortiz, M., Martin, J.B., Simmetry-preserving return mapping algorithms and minimum work paths: A unification of concepts, Int. J. Numer. Methods Eng., 28 (1989) 1839–1853. [7] Han, W., Reddy, B.D., Plasticity: Mathematical Theory and Numerical Analysis, Interdisciplinary Applied Mathematics: Mechanics and Materials, vol. 9. Springer, New York, (1999). [8] Simo, J.C., Hughes, T.J.R., Computation Inelasticity, Springer, New York, (1998). [9] Simo, J.C., Numerical Analysis of classical plasticity, In Handbook for Numerical Analysis, Ciarlet PG, Lions JJ (eds.), vol. IV, Elsevier, Amsterdam, (1998). [10] de Souza Neto, E.A., Perić, D., Owen, D.R.J., Computational methods for plasticity: Theory and applications, John Wiley & Sons, Ltd, Chichester, (2008). A T