Abstract
This chapter presents an overview of the theory of classical elastoplasticity and associated variational problems. The flow theory is presented as a normality relation for a convex yield function, or equivalently in terms of the dissipation function. The latter formulation provides the basis for the variational theory, for which results on well-posedness are presented. Predictor-corrector algorithms based on the time-discrete problem are reviewed. Aspects of the large-deformation theory, including algorithmic aspects, are also presented.
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Notes
- 1.
Non-associative laws are important in certain applications. Two examples are the Mohr–Coulomb and Drucker–Prager laws, which are used to model plastic behaviour in materials such as concrete, soil, and rock; see for example Lubliner (1990) for a summary account. The theory corresponding to non-associative flow laws is more complex and requires a distinct setting.
- 2.
For details of function spaces see Chap. Functional Analysis, Boundary Value Problems and Finite Elements.
References
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Acknowledgments
The support of the South African Department of Science and Technology and National Research Foundation through the South African Research Chair in Computational Mechanics is gratefully acknowledged.
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© 2016 CISM International Centre for Mechanical Sciences
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Reddy, B.D. (2016). Theoretical and Numerical Elastoplasticity. In: Schröder, J., Wriggers, P. (eds) Advanced Finite Element Technologies. CISM International Centre for Mechanical Sciences, vol 566. Springer, Cham. https://doi.org/10.1007/978-3-319-31925-4_7
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DOI: https://doi.org/10.1007/978-3-319-31925-4_7
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