SlipStrengthSlipRule¶

Overview¶

These objects provide a relation between the stress, history, and temperature and the slip rate on each individual slip system where the slip rate is related to the resolved shear stress on the system

$\tau_{g,i} = \bm{\sigma} : \left(\mathbf{d}_{g,i}\otimes\mathbf{n}_{g,i}\right)$

where $\mathbf{d}_{g,i}$ is the slip direction for group g, system i in the current coordinates and $\mathbf{n}_{g,i}$ is similarly the slip system normal. The interface used is:

$\dot{\gamma}_{g,i}, \frac{\partial \dot{\gamma}_{g,i}}{\partial \tau_{g,i}}, \frac{\partial \dot{\gamma}_{g,i}}{\partial \bar{\tau}_{g,i}} \leftarrow \mathcal{G}\left( \tau_{g,i}, \bar{\tau}_{g,i}, \bm{\alpha}, T \right) \dot{\mathbf{h}}, \frac{\partial \dot{\mathbf{h}}}{\partial \bm{\sigma}}, \frac{\partial \dot{\mathbf{h}}}{\partial \mathbf{h}} \leftarrow \mathcal{H}\left(\bm{\sigma}, \mathbf{h}, \bm{\alpha}, T \right)$

where $g$ indicates the slip group, $i$ indicates the system within the group, and $\bar{\tau}_{g,i}$ is the slip system strength, defined by a SlipHardening model:

SlipHardening

The definition of the history evolution is left to the SlipHardening model.

Implementations¶

PowerLawSlipRule

Parameters¶

Parameter	Object type	Description	Default
`strength`	`neml::SlipHardening`	Slip hardening definition	No

Class description¶

class SlipStrengthSlipRule : public neml::SlipMultiStrengthSlipRule ¶

Class where all slip rules that give the system response proportional to some strength, which is in turn a function of the history

Subclassed by neml::ArrheniusSlipRule, neml::PowerLawSlipRule

Public Functions

SlipStrengthSlipRule(ParameterSet &params)¶: Initialize with the strength model.

virtual double sslip(size_t g, size_t i, double tau, std::vector<double> strengths, double T) const¶: The slip rate on group g, system i given the resolved shear, the strength, and temperature

virtual double d_sslip_dtau(size_t g, size_t i, double tau, std::vector<double> strengths, double T) const¶: Derivative of slip rate with respect to the resolved shear.

virtual std::vector<double> d_sslip_dstrength(size_t g, size_t i, double tau, std::vector<double> strengths, double T) const¶: Derivative of the slip rate with respect to the strengths.

virtual double scalar_sslip(size_t g, size_t i, double tau, double strength, double T) const = 0¶: The scalar equivalent of the slip rates.

virtual double scalar_d_sslip_dtau(size_t g, size_t i, double tau, double strength, double T) const = 0¶: Derivative of slip rate with respect to the resolved shear.

virtual double scalar_d_sslip_dstrength(size_t g, size_t i, double tau, double strength, double T) const = 0¶: Derivative of the slip rate with respect to the strength.