Clay Exponential Plasticity

The Clay Exponential Plasticity model:

describes the inelastic behavior of the material by a yield function that depends on the three stress invariants, an associated flow assumption to define the plastic strain rate, and a strain hardening theory that changes the size of the yield surface according to the inelastic volumetric strain;
has an isotropic yield function and an exponential hardening law;
can be used only in an implicit analysis; and
requires that the elastic part of the deformation be defined by using the porous elastic material model within the same material definition.

Clay Exponential Plasticity

This option is used to define the yield surface and flow potential parameters for elastic-plastic materials that use the Clay Exponential Plasticity model.

You can specify an alternative to the direct specification of the initial yield surface size, $a_{0}$ . Set this parameter equal to $e_{1}$ , the intercept of the virgin consolidation line with the void ratio axis in a plot of void ratio versus the logarithm of pressure stress.

The size of the yield surface at any time is determined by the initial value of the hardening parameter, $a_{0}$ , and the amount of inelastic volume change that occurs according to the equation

a = a_{0} \exp [(1 + e_{0}) \frac{1 - J^{p l}}{λ - κ J^{p l}}]

where $J^{p l}$ is the inelastic volume change, $κ$ is the logarithmic bulk modulus of the material defined for the porous elastic material behavior, $λ$ is the logarithmic hardening constant defined for the clay plasticity material behavior; and $e_{0}$ is the initial void ratio.


Input Data	Description
Logarithmic Plastic Bulk Modulus	Logarithmic plastic bulk modulus, $λ$ .
Stress Ratio	Stress ratio at critical state, $M$ .
Initial Yield Surface Size	Initial yield surface size, $a_{0}$ .
Yield Surface	$β$ , the parameter defining the size of the yield surface on the “wet” side of the critical state.
Ratio Flow Stress	$K$ , the ratio of the flow stress in triaxial compression. If creep material behavior is included, $0.778 \leq K \leq 1$ . I
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

The hardening parameter $a_{0}$ can be defined indirectly by specifying $e_{1}$ , which is the intercept of the virgin consolidation line with the void ratio axis in the plot of void ratio, $e$ , versus the logarithm of the effective pressure stress, $\ln (p)$ . If this method is used $a_{0}$ is defined as

a_{0} = \frac{1}{2} \exp (\frac{e_{1} - e_{0} - κ \ln (p_{0})}{λ - κ})


Input Data	Description
Use Intercept	Used as an alternative to the direct specification of the initial yield surface size, $a_{0}$ . Set this parameter equal to $e_{1}$ , the intercept of the virgin consolidation line with the void ratio axis in a plot of void ratio versus the logarithm of pressure stress.