Keywords: CPPM, finite difference approximation, principal stress, plasticity.

Advanced inelastic constitutive models for pressure-sensitive media often fail to achieve wide usage, not because of their inappropriateness, but because the algorithms associated with their implementation are often far too lengthy and over-complex. Here the aim is to present a C₂ plasticity model (recently developed for structural concrete [1]) in as compact a form as possible. The isotropically hardening and kinematically softening 3D formulation relies upon a number of stress integration techniques (line search, sub-incrementation, use of auxiliary surface and CPPM) to ensure that stresses remain on the evolving yield surface.

This paper provides the matlab script for the model. The code employs finite difference approximations to the derivatives and operates with the principal components (generalised states are handled by appropriate transformations). The form of the algorithm leads itself to its direct implementation in a general purpose nonlinear finite element analysis package. Comparisons with established multiaxial experimental data from the University of Colorado [2] are given to illustrate the capabilities of the formulation. It has been shown that the model is able to simulate a range of proportional and non-proportional stress paths.

The matlab script determines eps (current strains), epsp (current plastic strains), kc (current hardening-softening parameter), sig (current stresses), given the material constants, and following variables: previous strains eps, previous plastic strains epsp, previous hardening/softening parameter kc and strain increment deps . This is achieved by calling the function subinc, in which the sub-incrementation method is applied. The sequence of calling the functions is shown in the full paper. The other functions are now described.

CPP: computes epsp, kc and sig using the CPPM.

lsrch: computes the line search parameter. A line search technique (together with enforcement of satisfaction of Goldstein's condition) is applied to the standard CPPM to speed up the solution process and ensure that global convergence is achieved.

df_dff: numerically computes the first derivatives dfdsig, dfds (plus hfun) and second derivatives d2fdsig2, d2fdsigds, dhdsig (plus dhds).

1

Li T. and Crouch R., "Konik: a concrete plasticity model", Proceedings of the 13th Annual National Conference of the UK Association of Computational Mechanics in Engineering, Sheffield, U.K., 21-22 March 2005.

2

Scavuzzo R., Stankowski T., Gerstle K.H. and Ko H.Y., "Stress-strain curves for concrete under multiaxial load history", NSF CME-80-01508, Department of Civil Engineering, University of Colorado, Boulder, 1983.

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