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Article

Open Access

Machine Recognition of Elastoplastic Materials in Material Genetics

Author(s)

P. A. Belov¹, N. Ya. Golovina² and Elliot Weiss³

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DOI:10.17265/1934-7359/2026.10.001

Affiliation(s)

1. Institute of Applied Mechanics of the Russian Academy of Sciences, Moscow 125040, Russia 2. Industrial University of Tyumen (IUT), Surgut Branch, Surgut 628400, Tyumen Region, Russia 3. Independent Researcher, USA

ABSTRACT

The studies [12, 13] separated two levels of material identification: Geometry Builder determines the morphology and the localC0/C1/C2 class structure of the deformation curve, whereas Material Builder solves the first physical inverse problem for a fixed architecture. The present work combines these levels into a machine-recognition problem in which the architecture and the observable physical passport are mutually dependent variables. The main theoretical result is a finite-dimensional reduction of the physically generalized Reinsch principle for an irreversible material. After the solution is represented in the genetic basis, the reversible integrals and antisymmetric Pfaffian channels are analytically integrated with respect to strain and condensed into segment matrices. The resulting target form is analogous to the Ritz method in its finite-dimensional reduction mechanism, but differs in the underlying principle: stationarity of a nonintegrable variational Pfaffian form is required instead of stationarity of potential energy. At each step of the deterministic genealogy, the point of maximum absolute defect specifies the reproduction location, while the profiled Ritz-Reinsch form selects the physically preferable admissible pair of offspring classes after closure of the observable Material Passport. For a prescribed experimental resolutionδ, the recognition result is the first genealogical state satisfyingERMS ≤δ andE∞ ≤δ. The resulting model is therefore not claimed to be the global minimum among all conceivable partitions; it is the least-complex experimentally admissible state of the deterministic Recognition genealogy.

KEYWORDS

Material genetics, machine recognition, morphology, model architecture, first inverse problem, approximation spline, Material Passport, generalized Reinsch principle, Pfaffian form, design of experiments, Geometry Builder, Material Builder.

Cite this paper

P. A. Belov , N. Ya. Golovina and Elliot Weiss . (2026). Machine Recognition of Elastoplastic Materials in Material Genetics, October 2026, Vol. 20, No. 10, 417-436.

References

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[8] Belov, P. A. 2026. “Foundations of the Genetics of Elastoplastic Materials.” Journal of Civil Engineering and Architecture 20: 129-46. doi:10.17265/1934-7359/2026.04.001.

[9] Belov, P. A., and Golovina, N. Ya. 2026. “Structural Theory of Elastoplastic Material Models.” Journal of Civil Engineering and Architecture 20: 281-91. doi:10.17265/1934-7359/2026.07.003.

[10] Belov, P. A., and Weiss, E. 2026. “Direct and First Inverse Problems of Genetic Identification of Materials at a Fixed Smoothness Class.” Journal of Civil Engineering and Architecture 20: 322-39. doi:10.17265/1934-7359/2026.08.002.

[11] Belov, P. A., and Weiss, E. 2026. “The Second Inverse Problem of Genetic Identification of Materials: Selection of the Optimal Model Architecture.” Journal of Civil Engineering and Architecture 20: 347-58. doi:10.17265/1934-7359/2026.08.004.

[12] Belov, P. A., Golovina, N. Ya., and Weiss, E. 2026. “Morphology of the Deformation Curve of Elastoplastic Materials.” Journal of Civil Engineering and Architecture 20: 385-99. doi:10.17265/1934-7359/2026.09.003.

[13] Belov, P. A., Golovina, N. Ya., and Weiss, E. 2026. “Physical Property Passport in the Genetics of Elastoplastic Materials.” Journal of Civil Engineering and Architecture 20: 400-16. doi:10.17265/1934-7359/2026.09.004.

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