CycLiqCP Material (Cyclic ElasticPlasticity)

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This command is used to construct a multi-dimensional material object that that follows the constitutive behavior of a cyclic elastoplasticity model for large post- liquefaction deformation.

nDmaterial CycLiqCP $matTag $G0 $kappa $h $Mfc $dre1 $Mdc $dre2 $rdr $alpha $dir $ein <$rho>

CycLiqCP material is a cyclic elastoplasticity model for large post-liquefaction deformation, and is implemented using a cutting plane algorithm. The model is capable of reproducing small to large deformation in the pre- to post-liquefaction regime. The elastic moduli of the model are pressure dependent. The plasticity in the model is developed within the framework of bounding surface plasticity, with special consideration to the formulation of reversible and irreversible dilatancy.

The model does not take into consideration of the state of sand, and requires different parameters for sand under different densities and confining pressures. The surfaces (i.e. failure and maximum pre-stress) are considered as circles in the pi plane.

The model has been validated against VELACS centrifuge model tests and has used on numerous simulations of liquefaction related problems.

When this material is employed in regular solid elements (e.g., FourNodeQuad, Brick), it simulates drained soil response. When solid-fluid coupled elements (u-p elements and SSP u-p elements) are used, the model is able to simulate undrained and partially drained behavior of soil.

During the application of gravity load (and static loads if any), the user is suggested to set the material behavior to be linear elastic, with the updateMaterialStage command:

updateMaterialStage -material $matTag -stage 0

After the gravity load stage, the material stage should be updated to achieve the desired elastic-plastic stress-strain response.

updateMaterialStage -material $matTag -stage 1

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$matTag	integer tag identifying material
$G0	A constant related to elastic shear modulus
$kappa	A constant related to elastic bulk modulus
$h	Model parameter for plastic modulus
$Mfc	Stress ratio at failure in triaxial compression
$dre1	Coefficient for reversible dilatancy generation
$Mdc	Stress ratio at which the reversible dilatancy sign changes
$dre2	Coefficient for reversible dilatancy release
$rdr	Reference shear strain length
$alpha	Parameter controlling the decrease rate of irreversible dilatancy
$dir	Coefficient for irreversible dilatancy potential
$ein	Initial void ratio
$rho	Saturated mass density

The material formulations for the CycLiqCP object are "ThreeDimensional" and "PlaneStrain".

NOTES:

1. The elastic modulii are given by the following relations:

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REFERENCES: Zhang J.M. and Wang G., 2012, “Large post-liquefaction deformation of sand, part I: physical mechanism, constitutive description and numerical algorithm”, Acta Geotechnica.

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Code Developed by: Rui Wang, Tsinghua University