Constitutive discovery now asks which variable drives which mechanism: climate-chamber interventions recover the true graph in 7 of 10 runs, observational data in none

The target of constitutive model discovery shifts from fitting responses to identifying the parent set of each mechanism, meaning which environmental variable or internal state directly drives it. Earlier EUCLID-family methods select sparse terms from a library under weak-form equilibrium with a fixed set of input variables per mechanism, so environmental dependencies enter only as additional regressors and the result is a correlational summary of the training protocol. In a synthetic perforated plate of a hygro-thermo-viscoelastic damaging material, 8 of 13 candidate edges are true; at about 0.01 px displacement noise the interventional protocol recovers the true graph exactly in 7 of 10 runs and the observational protocol in none, with mean structural Hamming distances of 0.4 and 3.2.

Candidate mechanism graphs are scored through the boundary value problem, so neither stresses nor internal variables need to be measured. Causal discovery methods generally assume every node is observed or that latent variables enter through simple noise models; in solid mechanics the decisive stress, damage and viscous strain are fields accessible only through a boundary value problem. The score uses only full-field displacements, reaction forces and environmental fields: strain-driven integration along measured displacements forms a residual from the weak-form equilibrium gap and reaction-force balance, evaluated on a plate with 528 nodes, 960 linear triangles and 1056 degrees of freedom.

Climate-chamber protocols are treated as interventions, and the Gauss–Newton matrix of the score serves as a local identifiability certificate and drives a greedy D-optimal test design. Under observational protocols temperature and moisture co-vary, and along the collinear directions the score barely distinguishes models; the matrix, computed exactly by automatic differentiation, is 250 to 380 times flatter along those directions for the observational protocol than for the interventional one. A greedy design started from observational data alone ranks second or third among all 126 four-test subsets for three different starting models, while the hand-designed interventional protocol ranks 62nd.

The demonstrated setting is a synthetic perforated plate of a hygro-thermo-viscoelastic damaging material, with data generated by the same model class that is searched and a truth additive in temperature and moisture; the intended readers are researchers in constitutive model discovery and experimental mechanics.

The certificate predicts attribution errors caused by collinear parents but not the bias that measurement noise induces in the weak-form score; at 0.03 px noise every protocol produced false edges. The lagged and instantaneous damage–relaxation edges are indistinguishable at the time resolution used, and the acyclicity constraint selects the lagged edge by the assumption that the material update has an explicit order of evaluation, not as an empirical finding.