Constitutive history is isolated from tentative Newton iterations so a rejected increment cannot become the accepted history.
01 Model and scope
Path-dependent material history is evaluated from the last committed state while Newton tests temporary trial states. Commit occurs only after the increment converges; rollback restores the accepted history after rejection so a failed trial cannot contaminate a retry.
Route assumptions and calculation checks
- Schema-v2 checkpoints and deterministic digests exist only for selected routes.
- Do not infer contact, distributed, or nonlinear-transient restart support from shared transaction primitives.
- Keep solver status and maturity verdict separate in every result.
Useful foundations and prerequisites
02 Essential equations and symbols
Definitions and conventions
- Sₙ
- Accepted history at the beginning of the increment.
- S*
- Temporary trial history.
- Trial strain increment.
- Accept converged history or discard rejected trial changes.
03 Step by step derivation
Follow the assumptions, equations and discrete operations in order. The full explanation stays visible.
1 · Freeze the committed state at increment start
A path-dependent law carries plastic strain, hardening variables, or other history from the last converged increment. Every Newton trial in the current increment starts from that same accepted state; trial-to-trial accumulation would make the result depend on the number of iterations.
2 · Evaluate a temporary constitutive trial
Given a trial strain increment, compute candidate stress, tangent, and state without mutating the committed record. Global equilibrium may request many such evaluations while testing corrections and line-search scales.
3 · Commit only after global convergence
When the full nonlinear increment satisfies its equilibrium and step criteria, promote the converged trial state to the next accepted history. Persist the resulting state and deterministic digest only through the supported checkpoint route.
4 · Roll back a rejected trial
If line search or cutback rejects the increment, discard every trial history and restore S_n before retrying. Checkpoint schema, digest determinism, and material-state transport are route-specific; shared transaction machinery does not establish restart for all contact, MPI, or transient combinations.
04 Algorithm and implementation
Read the linked versioned source for the actual assembly and solver behavior. The derivation above explains the mathematics and is not a verbatim source excerpt.
05 Verification and limitations
IMPLEMENTED ON DECLARED ROUTES · restart route-dependent
The formulation and its explanatory checks do not by themselves establish a qualified application domain. Consult the capability matrix and the applicable recorded case.