# The Damage Library¶

double damage_weibull(const vec &stress, const double &damage, const double &alpha, const double &beta, const double &DTime, const string &criterion)

Provides the damage evolution $$\delta D$$ considering a Weibull damage law. It is given by : $$\delta D = (1-D_{old})*\Big(1-exp\big(-1(\frac{crit}{\beta})^{\alpha}\big)\Big)$$ Parameters of this function are: the stress vector $$\sigma$$, the old damage $$D_{old}$$, the shape parameter $$\alpha$$, the scale parameter $$\beta$$, the time increment $$\Delta T$$ and the criterion (which is a string).

The criterion possibilities are : “vonmises” : $$crit = \sigma_{Mises}$$ “hydro” : $$crit = tr(\sigma)$$ “J3” : $$crit = J3(\sigma)$$ Default value of the criterion is “vonmises”.

double varD = damage_weibull(stress, damage, alpha, beta, DTime, criterion);

double damage_kachanov(const vec &stress, const vec &strain, const double &damage, const double &A0, const double &r, const string &criterion)

Provides the damage evolution $$\delta D$$ considering a Kachanov’s creep damage law. It is given by : $$\delta D = \Big(\frac{crit}{A_0(1-D_{old})}\Big)^r$$ Parameters of this function are: the stress vector $$\sigma$$, the strain vector $$\epsilon$$, the old damage $$D_{old}$$, the material properties characteristic of creep damage $$(A_0,r)$$ and the criterion (which is a string).

The criterion possibilities are : “vonmises” : $$crit = (\sigma*(1+\varepsilon))_{Mises}$$ “hydro” : $$crit = tr(\sigma*(1+\varepsilon))$$ “J3” : $$crit = J3(\sigma*(1+\varepsilon))$$ Here, the criterion has no default value.

double varD = damage_kachanov(stress, strain, damage, A0, r, criterion);

double damage_miner(const double &S_max, const double &S_mean, const double &S_ult, const double &b, const double &B0, const double &beta, const double &Sl_0)

Provides the constant damage evolution $$\Delta D$$ considering a Woehler- Miner’s damage law. It is given by : $$\Delta D = \big(\frac{S_{Max}-S_{Mean}+Sl_0*(1-b*S_{Mean})}{S_{ult}-S_{Max}}\big)*\big(\frac{S_{Max}-S_{Mean}}{B_0*(1-b*S_{Mean})}\big)^\beta$$ Parameters of this function are: the max stress value $$\sigma_{Max}$$, the mean stress value $$\sigma_{Mean}$$, the “ult” stress value $$\sigma_{ult}$$, the $$b$$, the $$B_0$$, the $$\beta$$ and the $$Sl_0$$.

Default value of $$Sl_0$$ is 0.0.

double varD = damage_minerl(S_max, S_mean, S_ult, b, B0, beta, Sl_0);

double damage_manson(const double &S_amp, const double &C2, const double &gamma2)

Provides the constant damage evolution $$\Delta D$$ considering a Coffin-Manson’s damage law. It is given by : $$\Delta D = \big(\frac{\sigma_{Amp}}{C_{2}}\big)^{\gamma_2}$$ Parameters of this function are: the “amp” stress value $$\sigma_{Amp}$$, the $$C_2$$ and the $$\gamma_2$$.

double varD = damage_manson(S_amp, C2, gamma2);