Model: Modified Cam-Clay
This model may be used to represent a solid material with plastic response to loading according to the Modified Cam-Clay (MCC) critical state model. The MCC yield function is defined as:
where \(p_c\) is the preconsolidation pressure, and \(M\) is the slope of the critical state line (CSL). \(M\) can be related to the critical state friction angle \(\phi_{cs}\) as
Here \(f\) represents the yield surface, as shown in Figure 6.
Here we use a hyper-elastic constitutive law using the following elastic rate constitutive equation
where \(c_r > 0\) is the elastic compressibility index. The tangential elastic bulk modulus is \(K=- \frac{p}{c_r}\) and varies linearly with pressure. We assume a constant shear modulus, and can write stress invariants p and q as
where \(p_0\) is the reference pressure and \(\epsilon_{v0}\) is the reference volumetric strain. The hardening law is derived from the linear relationship between logarithm of specific volume and logarithm of preconsolidation pressure, as show in Figure 7.
The hardening law describes evolution of the preconsolidation pressure \(p_c\) as
where \(c_c\) is the virgin compressibility index and we have \(0 < c_r < c_c\).
Parameters
The supported attributes will be documented soon.
Example
<Constitutive>
<ModifiedCamClay name="mcc"
defaultDensity="2700"
defaultRefPressure="-1.0"
defaultRefStrainVol="0"
defaultShearModulus="200.0"
defaultPreConsolidationPressure="-1.5"
defaultCslSlope="1.2"
defaultRecompressionIndex="0.002"
defaultVirginCompressionIndex="0.003" />
</Constitutive>