An Improved Numerical Integration Algorithm For Elastoplastic Constitutive Equations

A simplified methodology is proposed for elastoplastic calculations which holds for associative models. It is based on the representation of the elastoplastic model based on a rotation of the principal stresses and the fact that, in such system of coordinates, the direction that minimizes the square of a distance between a trial stress and the plastic surface has the same direction as the plastic deformation evolution. Such an approach allows for the elastoplastic calculation of complex models to be simpler and more efficient computationally. The proposed methodology is verified by the application to the elastoplastic model of Sandler-DiMaggio.6419Souza Neto, E., Peric, D., Owen, D.R.J., (2008) Computational Methods for Plasticity, , John Wiley & Sons LtdChen, W.F., Han, D.J., (1988) Plasticity for Structural Engineers, , Springer-VerlagDiMaggio, F.L., Sandler, I., Material model for granular soils (1971) Eng Mech Div, 97 (3), pp. 935-950Devloo, P.R.B., PZ: an object oriented environment for scientific programming (1997) Comput Methods Appl Mech Eng, 150 (1-4), pp. 133-153Devloo, P.R.B., Object oriented tools for scientific computing (2000) Eng Comput, 46 (2), pp. 203-214Lainé, E., Vallée, C., Fortuné, D., Nonlinear isotropic constitutive laws: choice of the three invariants, convex potentials and constitutive inequalities (1999) Int J Eng Sci, 37 (15), pp. 1927-1941Borja, R.I., (2012) Plasticity Modeling & Computation, , Springer Science & Business MediaArmero, F., Pérez-Foguet, A., On the formulation of closest-point projection algorithms in elastoplasticity - Part I: The variational structure (2002) Int J Numer Methods Eng, 53 (2), pp. 297-329Armero, F., Pérez-Foguet, A., On the formulation of closest-point projection algorithms in elastoplasticity - Part II: Globally convergent schemes (2002) Int J Numer Methods Eng, 53 (2), pp. 331-374Foster, C.D., Regueiro, R.A., Fossum, A.F., Borja, R.I., Implicit numerical integration of a three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials (2005) Comput Methods Appl Mech Eng, 194, pp. 5109-5138Fossum, A.F., Fredrich, J.T., Cap plasticity models and compactive and dilatant pre-failure deformation (2000), 4th North American Rock Mechanics Symposium, Seatle, United States of AmericaFossum, A.F., Brannon, R.M., The Sandia Geomodel: Theory and Users Guide (2004), SAND Report, Sandia National LaboratoriesSandler, I.S., Rubin, D., An algorithm and a modular subroutine for the cap model (1979) Int J Numer Anal Methods Geomech, 3 (2), pp. 173-18