Abstract
Different from elastic materials, some materials, such as steels or aluminum alloys, show permanent deformation when a force larger than a certain limit (elastic limit) is applied and removed. A simple example is bending a paper clip. If a small force is applied and removed, the paper clip comes back to its initial geometry, but when the force is larger than the elastic limit (irreversible), it does not. In contrast to elasticity, this behavior of materials is called plasticity. Since these materials are initially elastic and then become plastic, this behavior of materials is called elastoplasticity, which is the main topic of this chapter.
The original version of this chapter was revised. An erratum to this chapter can be found at https://doi.org/10.1007/978-1-4419-1746-1_6
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Notes
- 1.
Although the iteration counter is different, it does not matter when the residual vanishes.
- 2.
The same symbol was used for the reduced invariant of the Cauchy–Green deformation tensor in Chap. 3. Since this symbol is widely used in the literature, it is kept here.
References
Simo JC, Govindjee S. Nonlinear B-stability and symmetric preserving return mapping algorithms for plasticity and viscoplasticity. Int J Numer Methods Eng. 1991;31:151–76.
Simo JC, Taylor RL. Consistent tangent operator for rate-independent elastoplasticity. Comput Methods Appl Mech Eng. 1985;48:101–18.
Hughes TJR, Winget J. Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. Int J Numer Methods Eng. 1980;15:1862–7.
Malvern LE. Introduction to mechanics of a continuous medium. Englewood-Cliff: Prentice-Hall; 1969.
Fish J, Shek K. Computational aspects of incrementally objective algorithms for large deformation plasticity. Int J Numer Methods Eng. 1999;44:839–51.
Simo JC. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Comp Methods Appl Mech Eng. 1992;99:61–112.
Lee EH. Elastic-plastic deformation at finite strains. J Appl Mech. 1969;36:1–6.
Simo JC, Taylor RL. Quasi-compressible finite elasticity in principal stretches. Continuum basis and numerical algorithms. Comput Methods Appl Mech Eng. 1991;85:273–310.
Prager W, Hodge PG. Theory of perfectly plastic solids. New York: Wiley; 1951.
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Kim, NH. (2015). Finite Element Analysis for Elastoplastic Problems. In: Introduction to Nonlinear Finite Element Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1746-1_4
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DOI: https://doi.org/10.1007/978-1-4419-1746-1_4
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