Foundations of the Genetics of Elastoplastic Materials

This paper develops a variational-spectral framework for describing stress–strain curves of elastoplastic materials. The proposed terminology is introduced not as an a priori metaphor, but as a compact language for mathematical objects that have already been constructed within the model. The starting point is a variational formulation leading to an Euler-Lagrange equation, an associated spectrum of admissible boundary conditions, and the corresponding solution space. We show that this differential equation already contains the principal information about the material: the order of the model, the set of governing parameters, the characteristic roots, and the resulting basis functions of the solution space. On this basis, the paper consistently introduces the function space of solutions, its basis elements, orthonormal rearrangements of that basis, and the coefficients in the stress expansion. Special attention is given to continuous phenotype adaptation, operator-governed adaptation, spiral structures in the internal coefficient space, the genetic interpretation of the model, and prospects for AI-based structural recognition of materials.