### Abstract

Many rigid plastic models, including models for soils and granular materials, are described by hyperbolic systems of equations. Solutions of boundary value problems for such models can include envelopes of characteristics. It has been already shown for several models that solutions can be singular in the vicinity of surfaces coinciding with such envelopes. In particular, the quadratic invariant of the strain rate tensor approaches infinity according to an inverse square root rule. It is evident that such behaviour of exact solutions can cause difficulties with their numerical approximation. Therefore, it is of importance to obtain the exact asymptotic representation of solutions near singular surfaces. In the present paper, the double slip and rotation model is considered. It is shown that plane strain solutions near envelopes of characteristics are singular and the asymptotic representation of solutions is given. In particular, it is demonstrated that the quadratic invariant of the strain rate tensor approaches infinity according to an inverse square root rule, as in the case of the classical rigid perfectly plastic potential model for pressure-independent materials.

Original language | English |
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Title of host publication | Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics |

Pages | 1664-1668 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2013 Nov 15 |

Event | 5th Biot Conference on Poromechanics, BIOT 2013 - Vienna, Austria Duration: 2013 Jul 10 → 2013 Jul 12 |

### Publication series

Name | Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics |
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### Other

Other | 5th Biot Conference on Poromechanics, BIOT 2013 |
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Country | Austria |

City | Vienna |

Period | 13-07-10 → 13-07-12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mechanics of Materials

### Cite this

*Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics*(pp. 1664-1668). (Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics). https://doi.org/10.1061/9780784412992.196

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*Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics.*Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics, pp. 1664-1668, 5th Biot Conference on Poromechanics, BIOT 2013, Vienna, Austria, 13-07-10. https://doi.org/10.1061/9780784412992.196

**Singular solutions in the mechanics of soils.** / Alexandrov, Sergei; Jeng, Yeau-Ren.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Singular solutions in the mechanics of soils

AU - Alexandrov, Sergei

AU - Jeng, Yeau-Ren

PY - 2013/11/15

Y1 - 2013/11/15

N2 - Many rigid plastic models, including models for soils and granular materials, are described by hyperbolic systems of equations. Solutions of boundary value problems for such models can include envelopes of characteristics. It has been already shown for several models that solutions can be singular in the vicinity of surfaces coinciding with such envelopes. In particular, the quadratic invariant of the strain rate tensor approaches infinity according to an inverse square root rule. It is evident that such behaviour of exact solutions can cause difficulties with their numerical approximation. Therefore, it is of importance to obtain the exact asymptotic representation of solutions near singular surfaces. In the present paper, the double slip and rotation model is considered. It is shown that plane strain solutions near envelopes of characteristics are singular and the asymptotic representation of solutions is given. In particular, it is demonstrated that the quadratic invariant of the strain rate tensor approaches infinity according to an inverse square root rule, as in the case of the classical rigid perfectly plastic potential model for pressure-independent materials.

AB - Many rigid plastic models, including models for soils and granular materials, are described by hyperbolic systems of equations. Solutions of boundary value problems for such models can include envelopes of characteristics. It has been already shown for several models that solutions can be singular in the vicinity of surfaces coinciding with such envelopes. In particular, the quadratic invariant of the strain rate tensor approaches infinity according to an inverse square root rule. It is evident that such behaviour of exact solutions can cause difficulties with their numerical approximation. Therefore, it is of importance to obtain the exact asymptotic representation of solutions near singular surfaces. In the present paper, the double slip and rotation model is considered. It is shown that plane strain solutions near envelopes of characteristics are singular and the asymptotic representation of solutions is given. In particular, it is demonstrated that the quadratic invariant of the strain rate tensor approaches infinity according to an inverse square root rule, as in the case of the classical rigid perfectly plastic potential model for pressure-independent materials.

UR - http://www.scopus.com/inward/record.url?scp=84887327860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887327860&partnerID=8YFLogxK

U2 - 10.1061/9780784412992.196

DO - 10.1061/9780784412992.196

M3 - Conference contribution

SN - 9780784412992

T3 - Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics

SP - 1664

EP - 1668

BT - Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics

ER -