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

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U2 - 10.1061/9780784412992.196

DO - 10.1061/9780784412992.196

M3 - Conference contribution

AN - SCOPUS:84887327860

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

T2 - 5th Biot Conference on Poromechanics, BIOT 2013

Y2 - 10 July 2013 through 12 July 2013

ER -