### MODELING THE BEHAVIOR OF THE PHYSICAL AND GEOMETRIC NON-LINEAR FUNCTIONAL HETEROGENEOUS MATERIALS

#### Abstract

*The work is devoted to the problem of modeling the behavior of functionally inhomogeneous materials with the properties of pseudo-elastic-plasticity under complex loads, in particular at large strains (up to 20%), when geometric nonlinearity in Cauchy relations must be taken into account. In previous works of the authors, functionally heterogeneous materials were studied in a geometrically linear formulation, which is true for small deformations (up to 7%). When predicting work with material at large deformations, it is necessary to take into account geometric nonlinearity in Cauchy relations.*

*Studying the behavior of bodies made of functionally heterogeneous materials under unsteady load requires the development of special approaches, methods and algorithms for calculating the stress-strain state. When constructing physical relations, it is assumed that the deformation at the point is represented as the sum of the elastic component, the jump in deformation during the phase transition, plastic deformation and deformation caused by temperature changes.*

*A physical relationship in a nonlinear setting is proposed for modeling the behavior of bodies made of functionally heterogeneous materials. Formulas are obtained that nonlinearly relate strain rates and Formulas are obtained that nonlinearly relate strain rates and displacement rates.*

*Keywords: mathematical modeling, functional heterogeneous materials, geometric nonlinearity, spline functions, pseudo-elastic plasticity, phase transitions*

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P. Steblyanko, K. Domichev, A. Petrov (2020) Innovative Solution in Modern Science Dubai 4(40), ТК Меganom LLC, p.5-17, DOI 10.26886/ISMS.2414-634X.4(40)2020.

DOI: https://doi.org/10.26886/2414-634X.1(45)2021.5

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