DangVan/README.md

Dang Van Criterion (Multiaxial Fatigue)

This module implements a practical version of the Dang Van criterion to assess multiaxial fatigue from a time series of stress states.

Inputs:
- stress_series: list of stress states over time
  - Either 3x3 tensors [[sxx, sxy, sxz], [syx, syy, syz], [szx, szy, szz]]
  - Or Voigt 6-component arrays [sxx, syy, szz, sxy, syz, sxz]
- a: material parameter (hydrostatic sensitivity)
- b: material endurance limit (threshold)

Algorithm:
- Hydrostatic stress: sigma_H(t) = trace(sigma)/3
- Deviatoric stress: s = sigma - sigma_H * I
- Von Mises: sigma_vm = sqrt(3/2 * s:s)
- Octahedral shear: tau_oct = sqrt(2)/3 * sigma_vm
- Dang Van value: DV(t) = tau_oct(t) + a * sigma_H(t)
- Safe if max_t DV(t) <= b

Returns:
- dv_max: maximum DV value
- safe: boolean
- margin: b - dv_max
- index_max: time index of max DV
- series: list of {time_index, dv, tau_oct, sigma_H}

Note:
- This is a practical engineering implementation. Exact microscopic shear on critical planes requires additional computations; octahedral shear is a standard invariant-based proxy.