### Abstract

Original language | English |
---|---|

Pages (from-to) | 347-362 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 103 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1993 |

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*Computer Methods in Applied Mechanics and Engineering*,

*103*(3), 347-362. https://doi.org/10.1016/0045-7825(93)90127-J

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*Computer Methods in Applied Mechanics and Engineering*, vol. 103, no. 3, pp. 347-362. https://doi.org/10.1016/0045-7825(93)90127-J

**A generalisation of J2-flow theory for polar continua.** / Borst, de, R.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - A generalisation of J2-flow theory for polar continua

AU - Borst, de, R.

PY - 1993

Y1 - 1993

N2 - A pressure-dependent J2-flow theory is proposed for use within the framework of the Cosserat continuum. To this end the definition of the second invariant of the deviatoric stresses is generalised to include couple-stresses, and the strain-hardening hypothesis of plasticity is extended to take account of micro-curvatures. The temporal integration of the resulting set of differential equations is achieved using an implicit Euler backward scheme. This return-mapping algorithm results in an exact satisfaction of the yield condition at the end of the loading step. Moreover, the integration scheme is amenable to exact linearisation, so that a quadratic rate of convergence is obtained when Newton's method is used. An important characteristic of the model is the incorporation of an internal length scale. In finite element simulations of localisation, this property warrants convergence of the load-deflection curve to a physically realistic solution upon mesh refinement and to a finite width of the localisation zone. This is demonstrated for an infinitely long shear layer and for a biaxial specimen composed of a strain-softening Drucker-Prager material.

AB - A pressure-dependent J2-flow theory is proposed for use within the framework of the Cosserat continuum. To this end the definition of the second invariant of the deviatoric stresses is generalised to include couple-stresses, and the strain-hardening hypothesis of plasticity is extended to take account of micro-curvatures. The temporal integration of the resulting set of differential equations is achieved using an implicit Euler backward scheme. This return-mapping algorithm results in an exact satisfaction of the yield condition at the end of the loading step. Moreover, the integration scheme is amenable to exact linearisation, so that a quadratic rate of convergence is obtained when Newton's method is used. An important characteristic of the model is the incorporation of an internal length scale. In finite element simulations of localisation, this property warrants convergence of the load-deflection curve to a physically realistic solution upon mesh refinement and to a finite width of the localisation zone. This is demonstrated for an infinitely long shear layer and for a biaxial specimen composed of a strain-softening Drucker-Prager material.

U2 - 10.1016/0045-7825(93)90127-J

DO - 10.1016/0045-7825(93)90127-J

M3 - Article

VL - 103

SP - 347

EP - 362

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

IS - 3

ER -