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Bifurcation Micromechanics in Granular Materials

Authors
  • Wautier, A.
  • Liu, J.
  • Nicot, Frédéric
  • Darve, F.
Publication Date
Jan 01, 2019
Identifiers
DOI: 10.1002/9781119579311.ch10
OAI: oai:HAL:hal-02608396v1
Source
HAL
Keywords
Language
English
License
Unknown
External links

Abstract

Plasticity, as induced by continuous irreversible rate‐independent strains, is present in many engineering and natural materials. In this large framework, granular materials play a specific role due to the non‐associated character of their plastic strains. This non‐associativeness is essentially due to a Mohr‐Coulomb plastic limit condition, which gives rise to conical shapes for both the elastic/yield surface and the plastic limit surface. In associated plasticity, the bifurcations correspond to the singularities of the constitutive elasto‐plastic matrix and thus to the vanishing of the determinant of this matrix on the plastic limit surface. On the contrary, in non‐associated plasticity, bifurcations and failures can largely occur before reaching the Mohr‐Coulomb plastic limit. This chapter focuses on the importance of the second‐order work criterion to detect the existence of an unstable state. The chapter shows how similar the micromechanics in homogeneous samples suffering from different patterns of failure are.

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