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Integration of Tresca and Mohr–Coulomb constitutive relations in plane strain elastoplasticity
Author(s) -
Sloan S. W.,
Booker J. R.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620330112
Subject(s) - constitutive equation , plane stress , mathematics , mohr–coulomb theory , constant (computer programming) , plane (geometry) , mathematical analysis , coulomb , finite element method , physics , geometry , computer science , thermodynamics , programming language , quantum mechanics , electron
This paper considers the problem of integrating the constitutive relations for Tresca and Mohr–Coulomb materials under conditions of plane strain. In the case of a Tresca material, we show that the constitutive law may be integrated exactly by assuming the strain rates dϵ/dλ to be constant. We also derive a semi‐analytic method for integrating both types of constitutive law which assumes that the quantities dϵ/dλ are constant. This approach is motivated by the fact that the exact variation of the strains during a time interval is unknown and leads to a single non‐linear equation in λ which can be solved efficiently to yield the unknown stresses. Finally, we compare the results from the analytic and semi‐analytic methods with those from a variety of numerical integration schemes.