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);