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Capturing strain localization in dense sands with random Jose E. Andrade, Ronaldo I. Borja,

Summary: Capturing strain localization in dense sands with random
Jos´e E. Andrade, Ronaldo I. Borja,
Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
This paper presents a three-invariant constitutive framework suitable for the numerical anal-
yses of localization instabilities in granular materials exhibiting unstructured random density.
A recently proposed elastoplastic model for sands based on critical state plasticity is enhanced
with the third stress invariant to capture the difference in the compressive and extensional
yield strengths commonly observed in geomaterials undergoing plastic deformation. The
new three-invariant constitutive model, similar to its two-invariant predecessor, is capable
of accounting for meso-scale inhomogeneities as well as material and geometric nonlinear-
ities. Details regarding the numerical implementation of the model into a fully nonlinear
finite element framework are presented and a closed-form expression for the consistent tan-
gent operator, whose spectral form is used in the strain localization analyses, is derived. An
algorithm based on the spectral form of the so-called acoustic tensor is proposed to search for
the necessary conditions for deformation bands to develop. The aforementioned framework is
utilized in a series of boundary-value problems on dense sand specimens whose density fields
are modeled as exponentially distributed unstructured random fields to account for the effect
of inhomogeneities at the meso-scale and the intrinsic uncertainty associated with them.


Source: Andrade, Jose - Department of Civil and Environmental Engineering, Northwestern University


Collections: Engineering