LANLTiModel¶

Overview¶

Forest dislocation density based hardening slip model, used to physically describe of dislocation dominant plastic deformation.

$\tau_{i}=\tau_{0,i}^{s}+X^{i}b^{i}\mu^{i}\sqrt{\rho_{for}^{i}}$

The forest dislocation density evloves with strain and varies with dislication trapping and annihilation rates of each slip system.

$\dot{\rho_{for}^{i}}=k_{1}^{i}\sqrt{\rho_{for}^{i}}-k_{2}^{i}\rho_{for}^{i}$

A pseudo-slip hardening model used to describe the resistance of the propagation of twinning.

$\tau_{i}=\tau_{0,i}^{t}+\mu{i}\sum_{j=1}^{n_{slip}} C^{ij}b^{i}b^{j}\rho_{for}^{j}$

where $i$ is the unrolled indices corresponding to slip group.

Parameter	Object type	Description	Default
`tau_0`	`std::vector<double>`	Initial strengths	N
`C_st`	`neml::SquareMatrix`	Twin-slip interaction matrix	N
`mu`	`std::vector<double>`	Elastic modulus on the system	N
`k1`	`std::vector<double>`	Coefficient for trapping of dislocation	N
`k2`	`std::vector<double>`	Coefficient for annihilation of dislocation	N
`X`	`double`	Dislocation interaction parameter	0.9
`inivalue`	`double`	Initial values of internal variables	1.0e-6

class LANLTiModel : public neml::SlipHardening ¶

Public Functions

virtual std::vector<std::string> varnames() const¶: Report your variable names.

virtual void set_varnames(std::vector<std::string> vars)¶: Set new varnames.

virtual void populate_hist(History &history) const¶: Request whatever history you will need.

virtual double hist_to_tau(size_t g, size_t i, const History &history, Lattice &L, double T, const History &fixed) const¶: Map the set of history variables to the slip system hardening.

virtual History d_hist_to_tau(size_t g, size_t i, const History &history, Lattice &L, double T, const History &fixed) const¶: Derivative of the map wrt to history.

virtual History hist(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &L, double T, const SlipRule &R, const History &fixed) const¶: The rate of the history.

virtual History d_hist_d_s(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &L, double T, const SlipRule &R, const History &fixed) const¶: Derivative of the history wrt stress.

virtual History d_hist_d_h(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &L, double T, const SlipRule &R, const History &fixed) const¶: Derivative of the history wrt the history.

virtual History d_hist_d_h_ext(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &L, double T, const SlipRule &R, const History &fixed, std::vector<std::string> ext) const¶: Derivative of this history wrt the history, external variables.

Public Static Functions

static std::unique_ptr<NEMLObject> initialize(ParameterSet &params)¶: Initialize from a parameter set.