Struct J2ConsistentTangent 

pub struct J2ConsistentTangent {
    pub shear_modulus: f64,
    pub bulk_modulus: f64,
    pub hardening_modulus: f64,
}

Full 6×6 algorithmic (consistent) tangent modulus for J2 plasticity with isotropic hardening, in Voigt notation.

The consistent tangent ensures quadratic convergence in Newton-Raphson FEM. It is defined as:

C_ep = C_e - (6G²)/(3G+H) * (n⊗n) / σ_y_trial² - 2G * Δγ/q_tr * (I_dev - n⊗n)

where n = s_trial / q_tr is the unit deviatoric stress direction, Δγ is the plastic consistency parameter, G is the shear modulus, H is the hardening modulus, and I_dev is the deviatoric projector.

For the elastic step, returns the elastic stiffness C_e.

Fields

shear_modulus: f64

Shear modulus G (Pa).

bulk_modulus: f64

Bulk modulus K (Pa).

hardening_modulus: f64

Isotropic hardening modulus H (Pa).

Implementations

impl J2ConsistentTangent

pub fn new( shear_modulus: f64, bulk_modulus: f64, hardening_modulus: f64, ) -> Self

Create a new J2 consistent tangent calculator.

pub fn from_young_poisson(E: f64, nu: f64, hardening_modulus: f64) -> Self

Create from Young’s modulus and Poisson’s ratio.

pub fn elastic_stiffness(&self) -> [f64; 36]

Elastic 6×6 stiffness in Voigt notation (isotropic).

Voigt order: [σ_xx, σ_yy, σ_zz, σ_yz, σ_xz, σ_xy].

pub fn compute_consistent_tangent( &self, trial_stress: &[f64; 6], delta_gamma: f64, ) -> [f64; 36]

Compute the consistent (algorithmic) tangent modulus.

Requires the trial stress, yield stress at start of increment, and whether plastic flow occurred.

Arguments

• trial_stress — trial Voigt stress [xx,yy,zz,yz,xz,xy]
• sigma_y — current yield stress (before increment)
• delta_gamma — plastic consistency parameter (0 if elastic)

Returns

6×6 consistent tangent (flat row-major).