Progress in Structural Engineering pp 407-421 | Cite as
Incremental Elastic-Ziegler Kinematic Hardening Plasticity Formulations and an Algorithm for the Numerical Integration with an “A Priori” Error Control
Abstract
The incremental elastic-plastic constitutive law with Ziegler kinematic hardening is presented in the form of a pair of dual Quadratic Programming (QP) Problems or the corresponding Linear Complementarity Problems (LCP) with reference to Maier’s work. The integration scheme is thought of as a two step algorithm: a predictor step described by the traditional LCP mentioned before, and a corrector step, interpreted as a neutral equilibrium phase described again as a pair of strictly convex minimum problems. Both steps assume the stress path to generate an error on the yield condition always lower than a prescribed tolerance. Applications are presented to compare the proposed scheme with other more traditional ones adopted by standard plasticity finite elements codes.
Keywords
Yield Surface Integration Scheme Linear Complementarity Problem Stress Path Kinematic HardeningPreview
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References
- [1]ABAQUS Theoretical and Example Problems Manual, Release 4. 7, Hibbitt, Karlsson & Sorensen, Inc., Providence, R.I., 1987.Google Scholar
- [2]Franchi, A., Genna, F., A Numerical Scheme for Integrating the Rate Plasticity equations with an “A Priori” Error Control, Computer Methods in Applied Mechanics and Engineering, 1987, 317–342.Google Scholar
- [3]Hodge, P. J. Jr., Automatic Piecewise Linearization in Ideal Plasticity, Computer Methods in Applied Mechanics and Engineering, 1977, 249–272.Google Scholar
- [4]Krieg, R. D., Krieg, D. B., Accuracies of Numerical Solution Methods for the Elastic-Perfectly Plastic Model, Transaction of the ASME, Vol. 99, No. 4, 1977, 510–515.Google Scholar
- [5]Maier, G., A Quadratic Programming Approach for Certain Classes of Non Linear Structural Problems, Meccanica, 1968, 121–130.Google Scholar
- [6]Maier, G., A Matrix Structural Theory of Piecewise Linear Elastoplasticity with Interacting Yield Planes, Meccanica, 1970, 54–66.Google Scholar
- [7]Schreyer, H. L., Kulak, R. F., and Kramer, J. K., Accurate Numerical Solutions for Elastic Plastic Models, Transaction of the ASME, Vol. 101, 1979, 226–235.Google Scholar
- [8]Franchi, A., Genna, F., Minimum Principles and Initial Stress Method in Elastic Plastic Analysis, Eng. Struct., 1984, 65–69.Google Scholar