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Structural Theory of Elastoplastic Material Models



Author(s)

Petr A. Belov1 and Natalia Ya. Golovina2

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DOI:10.17265/1934-7359/2026.07.003

1. Institute of Applied Mechanics, Russian Academy of Sciences, Moscow 125040, Russia 2. Tyumen Industrial University (TIU), Surgut Branch, Surgut 628400, Tyumen Region, Russia

This paper presents the second stage of a research program on the genetics of elastoplastic materials. The first article in the series introduced a genetic interpretation of the functional space spanned by the fundamental solutions of the constitutive differential equation governing a material model. In the present paper, the emphasis shifts from the terminology of genes, chromosomes, and phenotypes to a structural theory of elastoplastic material models. The central thesis is that the primary object of structural classification is not the observable deformation curve itself, but the ordinary differential equation governing the material model and the hereditary mathematical information encoded in that equation, from which the curve emerges as a phenotypic realization. The paper distinguishes between a phenotypic description, based on observable deformation curves, and a genotypic description, based on the smoothness class, characteristic spectrum, gene space, and governing ODE (Ordinary Differential Equation) of the material model. On this basis, the direct and inverse problems of materials genetics are reformulated. The direct problem is interpreted as the transition from the governing ODE of the material model to the observable deformation curve. The inverse problem is shown to have a two-level structure: spectral identification reconstructs the gene basis from the observed phenotype, whereas genotypic identification recovers the governing ODE of the material model from the smoothness class and the identified spectral structure. This distinction establishes a theoretical bridge between the published foundations of materials genetics and subsequent studies of canonical representation, analogical DNA portraits of materials, operator identification, computational spectral modules, and libraries of material genomes.

Materials genetics, structural theory, elastoplastic material model, deformation curve, governing ODE of the material model, gene space, phenotype, genotype, inverse problem, spectral identification, genotypic identification.

Petr A. Belov and Natalia Ya. Golovina. (2026). Structural Theory of Elastoplastic Material Models,  Journal of Civil Engineering and Architecture, July 2026, Vol. 20, No. 7, 281-291.