Struct GursonDamage 

pub struct GursonDamage {
    pub f: f64,
    pub f0: f64,
    pub fc: f64,
    pub f_f: f64,
    pub q1: f64,
    pub q2: f64,
    pub q3: f64,
    pub a_n: f64,
    pub eps_n: f64,
    pub s_n: f64,
}

Gurson-Tvergaard-Needleman (GTN) porous plasticity model.

Yield function: Φ = (σ_eq/σ_y)² + 2q₁f* cosh(3q₂σ_H/(2σ_y)) - 1 - (q₁f*)² = 0

where f* is the effective void volume fraction.

Fields

f: f64

Current void volume fraction f ∈ [0, 1].

f0: f64

Initial void volume fraction f_0.

fc: f64

Critical void volume fraction f_c for coalescence.

f_f: f64

Failure void volume fraction f_F.

q1: f64

Tvergaard parameter q₁ (typically 1.5).

q2: f64

Tvergaard parameter q₂ (typically 1.0).

q3: f64

Tvergaard parameter q₃ (typically q₁²).

a_n: f64

Nucleation amplitude A_n.

eps_n: f64

Mean nucleation strain ε_N.

s_n: f64

Standard deviation of nucleation s_N.

Implementations

impl GursonDamage

pub fn new(f0: f64, fc: f64, f_f: f64, a_n: f64, eps_n: f64, s_n: f64) -> Self

Create a new GTN model with default Tvergaard parameters.

pub fn effective_void_fraction(&self) -> f64

Effective void volume fraction f* accounting for coalescence.

f* = f if f <= f_c f* = f_c + (f̄_F - f_c)/(f_F - f_c) * (f - f_c) if f > f_c

where f̄_F = (q₁ + sqrt(q₁² - q₃))/q₃ ≈ 1/q₁

pub fn yield_function(&self, sigma_eq: f64, sigma_h: f64, sigma_y: f64) -> f64

Evaluate the GTN yield function.

Φ = (σ_eq/σ_y)² + 2q₁f* cosh(3q₂σ_H/(2σ_y)) - 1 - q₃f*²

pub fn nucleation_rate(&self, eps_p: f64, eps_p_dot: f64) -> f64

Void nucleation rate from strain-controlled nucleation (Chu & Needleman).

ḟ_nucleation = A_n / (s_N * sqrt(2π)) * exp(-0.5*((ε_p - ε_N)/s_N)²) * ε̇_p

pub fn growth_rate(&self, plastic_volumetric_strain_rate: f64) -> f64

Void growth rate from plastic dilatation.

ḟ_growth = (1 - f) * ε̇_kk^p

pub fn update( &mut self, eps_p: f64, eps_p_dot: f64, plastic_volumetric_strain_rate: f64, dt: f64, )

Update void volume fraction given plastic strain increment.

pub fn is_failed(&self) -> bool

Check if material has failed (f >= f_F).

pub fn compute_void_growth_rate( &self, sigma_h: f64, sigma_eq: f64, sigma_y: f64, deps_p: f64, ) -> f64

Compute the total void growth rate including nucleation and growth.

The Rice-Tracey void growth model extended for GTN:

ḟ_total = ḟ_growth + ḟ_nucleation

where:

• ḟ_growth = (1 - f) * A * sinh(B * η) * ε̇_p
• ḟ_nucleation = Gaussian nucleation from Chu-Needleman model
• η = σ_H / σ_eq (stress triaxiality)
• A = 0.283 (Rice-Tracey coefficient), B = 1.5 (triaxiality amplifier)

Arguments

• sigma_h - Hydrostatic (mean) stress [Pa]
• sigma_eq - Von Mises equivalent stress [Pa]
• sigma_y - Current yield stress [Pa]
• deps_p - Equivalent plastic strain increment (dimensionless)

Returns

Total void volume fraction rate df/dε (per unit plastic strain)

Trait Implementations

impl Clone for GursonDamage

fn clone(&self) -> GursonDamage

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for GursonDamage

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.