CycLiqCPSP Material

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This command is used to construct a multi-dimensional material object based on a unified plasticity model for large post-liquefaction shear deformation of sand.

nDmaterial CycLiqCPSP $matTag $G0 $kappa $h $M $dre1 $dre2 $rdr $alpha $dir $lambdac $ksi $e0 $np $nd $ein <$rho>

CycLiqCPSP material is a constitutive model for sand with special considerations for cyclic behaviour and accumulation of large post-liquefaction shear deformation, and is implemented using a cutting plane algorithm. The model: (1) achieves the simulation of post-liquefaction shear deformation based on its physics, allowing the unified description of pre- and post-liquefaction behavior of sand; (2) directly links the cyclic mobility of sand with reversible and irreversible dilatancy, enabling the unified description of monotonic and cyclic loading; (3) introduces critical state soil mechanics concepts to achieve unified modelling of sand under different states.

The critical, maximum stress ratio and reversible dilatancy surfaces follow a rounded triangle in the pi plane similar to the Matsuoka-Nakai criterion.

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 non-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

If a linear elastic stage is required, it can be achieved through:

updateMaterialStage -material $matTag -stage 2

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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
$M	Critical state stress ratio
$dre1	Coefficient for reversible dilatancy generation
$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
$lambdac	Critical state constant
$ksi	Critical state constant
$e0	Void ratio at pc=0
$np	Material constant for peak mobilized stress ratio
$nd	Material constant for reversible dilatancy generation stress ratio
$ein	Initial void ratio
$rho	Saturated mass density

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

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REFERENCES: Wang R., Zhang J.M., Wang G., 2014. A unified plasticity model for large post-liquefaction shear deformation of sand. Computers and Geotechnics. 59, 54-66.

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Code Developed by: Rui Wang, Tsinghua University