Singular solutions in the mechanics of soils

Sergei Alexandrov, Yeau-Ren Jeng

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationPoromechanics V - Proceedings of the 5th Biot Conference on Poromechanics
Pages1664-1668
Number of pages5
DOIs
Publication statusPublished - 2013 Nov 15
Event5th Biot Conference on Poromechanics, BIOT 2013 - Vienna, Austria
Duration: 2013 Jul 102013 Jul 12

Publication series

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

Other

Other5th Biot Conference on Poromechanics, BIOT 2013
CountryAustria
CityVienna
Period13-07-1013-07-12

Fingerprint

Mechanics
Soils
Tensors
Strain rate
Plastics
Granular materials
Boundary value problems

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials

Cite this

Alexandrov, S., & Jeng, Y-R. (2013). Singular solutions in the mechanics of soils. In 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
Alexandrov, Sergei ; Jeng, Yeau-Ren. / Singular solutions in the mechanics of soils. Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics. 2013. pp. 1664-1668 (Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics).
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Alexandrov, S & Jeng, Y-R 2013, Singular solutions in the mechanics of soils. in 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.

Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics. 2013. p. 1664-1668 (Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Alexandrov S, Jeng Y-R. Singular solutions in the mechanics of soils. In Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics. 2013. p. 1664-1668. (Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics). https://doi.org/10.1061/9780784412992.196