Constant-stress creep update: small-increment precision

Review of the public Kachanov–Rabotnov material-point path found cancellation in the exact update, not an error in its constitutive equations. With the reviewed 650 C coefficients, 110 MPa and a 1e-12 h interval, the previous implementation returned zero strain and damage increments. The independent 90-digit reference gives approximately 1.3483637994e-17 and 2.7625999849e-17, respectively.

Numerical design

For old integrity I=1-D, power p=phi+1 and normalized stress s, retain f=p B s^m dt/I^p and evaluate log(I_new/I)=log1p(-f)/p. Compute integrity loss and the integrated creep increment using expm1, rather than differences between powers near one. These are standard cancellation-resistant primitives; see the Python math reference. No coefficients, exponent, stress measure or time unit change.

The same audit found cancellation in PowerLawCreep.constant_stress_increment: at a stored start time of 1e10, end time start + 1e-5, coefficient 1e-12, stress exponent 3 and stress 100, subtracting accumulated strains underestimates the interval increment by 4.63%. The actual representable duration is 9.5367431640625e-6; this is the reference interval, not an assumption that floating-point time has retained all requested decimal digits. For time-independent rates, integrate rate times duration directly. Otherwise, factor the power difference around the upper endpoint and use a bounded -expm1(-p*log(end/start)) fraction with log1p for nearby endpoints. Zero-origin and zero-duration paths remain explicit; invalid clocks are rejected. This avoids cancellation without changing the power-law integral or resetting the physical clock.

The same expression stabilizes the prescribed failure threshold and rupture time. A supplied terminal state remains terminal instead of losing damage when the configured threshold is lower than its existing damage. This remains a bounded constant-stress material-point model, not a new global damage solver.

Acceptance

The dedicated tests compare a 90-digit Decimal integration at small and ordinary increments, positive/negative/zero integral exponents, nonzero prior damage, tensor direction, repeated subdivision, explicit stress/time reference scales, tiny failure thresholds, and terminal-state monotonicity. Existing constitutive, analytical structural references and release golden contracts are also checked. After adding the power-law repair, 184 targeted tests passed, including the actual thermal-wall example, creep history, manufactured field, elastic follow-up and prescribed-trial paths. The 47 dedicated precision tests also cover wide time intervals, nearly singular integrable initial rates, zero duration and the distinction between requested and representable clocks. An additional zero-damage/high-power underflow regression passes in a 92-test material-reference run. It keeps the zero-damage branch independent of the unused damage exponent and avoids dividing by an underflowed integrity power. Critical lint passes. This numerical repair does not resolve discrepancies in published material coefficients or qualify P92 engineering life.