Superimposed viscoplastic flow rule¶

Overview¶

This model sums the contribution of multiple individual viscoplastic hardening rules according to the relations:

$\dot{\gamma} = \sum_{i=1}^{n_{models}} \dot{\gamma}_i \mathbf{g}_{...} = \frac{1}{\dot{\gamma}} \sum_{i=1}^{n_{models}} \dot{\gamma}_i \mathbf{g}_{...,i} \mathbf{h}_{...} = \bigoplus_{i=1}^{n_{models}} \mathbf{h}_{...,i}$

where $...$ here is all of $\gamma$ , $t$ , and $T$ and $\oplus$ represents concatenation. The internal variables is then the set of all variables maintained by each individual flow rule (and these variables cannot overlap).

Parameters¶

Parameter	Object type	Description	Default
`flow_rules`	`std::vector<neml::ViscoplasticFlowRule>`	List of individual flow rules	No

Class description¶

class SuperimposedViscoPlasticFlowRule : public neml::ViscoPlasticFlowRule ¶

Superimpose multiple flow rules into a composite model.

Public Functions

SuperimposedViscoPlasticFlowRule(ParameterSet &params)¶

size_t nmodels() const¶: Number of individual models being summed.

virtual void populate_hist(History &hist) const¶: Populate a blank history object.

virtual void init_hist(History &hist) const¶: Initialize history at time zero.

virtual void y(const double *const s, const double *const alpha, double T, double &yv) const¶: Scalar flow rate.

virtual void dy_ds(const double *const s, const double *const alpha, double T, double *const dyv) const¶: Derivative of scalar flow wrt stress.

virtual void dy_da(const double *const s, const double *const alpha, double T, double *const dyv) const¶: Derivative of scalar flow wrt history.

virtual void g(const double *const s, const double *const alpha, double T, double *const gv) const¶: Contribution towards the flow proportional to the scalar inelastic strain rate

virtual void dg_ds(const double *const s, const double *const alpha, double T, double *const dgv) const¶: Derivative of g wrt stress.

virtual void dg_da(const double *const s, const double *const alpha, double T, double *const dgv) const¶: Derivative of g wrt history.

virtual void g_time(const double *const s, const double *const alpha, double T, double *const gv) const¶: Contribution towards the flow proportional directly to time.

virtual void dg_ds_time(const double *const s, const double *const alpha, double T, double *const dgv) const¶: Derivative of g_time wrt stress.

virtual void dg_da_time(const double *const s, const double *const alpha, double T, double *const dgv) const¶: Derivative of g_time wrt history.

virtual void g_temp(const double *const s, const double *const alpha, double T, double *const gv) const¶: Contribution towards the flow proportional to the temperature rate.

virtual void dg_ds_temp(const double *const s, const double *const alpha, double T, double *const dgv) const¶: Derivative of g_temp wrt stress.

virtual void dg_da_temp(const double *const s, const double *const alpha, double T, double *const dgv) const¶: Derivative of g_temp wrt history.

virtual void h(const double *const s, const double *const alpha, double T, double *const hv) const¶: Hardening rate proportional to the scalar inelastic strain rate.

virtual void dh_ds(const double *const s, const double *const alpha, double T, double *const dhv) const¶: Derivative of h wrt stress.

virtual void dh_da(const double *const s, const double *const alpha, double T, double *const dhv) const¶: Derivative of h wrt history.

virtual void h_time(const double *const s, const double *const alpha, double T, double *const hv) const¶: Hardening rate proportional directly to time.

virtual void dh_ds_time(const double *const s, const double *const alpha, double T, double *const dhv) const¶: Derivative of h_time wrt stress.

virtual void dh_da_time(const double *const s, const double *const alpha, double T, double *const dhv) const¶: Derivative of h_time wrt history.

virtual void h_temp(const double *const s, const double *const alpha, double T, double *const hv) const¶: Hardening rate proportional to the temperature rate.

virtual void dh_ds_temp(const double *const s, const double *const alpha, double T, double *const dhv) const¶: Derivative of h_temp wrt. stress.

virtual void dh_da_temp(const double *const s, const double *const alpha, double T, double *const dhv) const¶: Derivative of h_temp wrt history.

Public Static Functions

static std::string type()¶: String type for the object system.

static std::unique_ptr<NEMLObject> initialize(ParameterSet &params)¶: Default parameters.

static ParameterSet parameters()¶: Initialize from parameters.