Mathematical model of plasticity for orthotropic composite materials under non-isothermal loading conditions

V. N. Zimin, D. R. Rakhimov, I. Yu. Savelyeva

Bauman Moscow State Technical University

Abstract: The article presents a mathematical model describing the nonlinear deformation of orthotropic composite materials under non-isothermal loading conditions. The model is based on a thermodynamic approach with internal state parameters, allowing for the consideration of microstructural changes in the material. The quantity, nature, and kinetic relationships of the internal parameters are defined. The governing equations and the heat conduction equation necessary for formulating a coupled thermoplastic boundary value problem have been derived. In a particular case, the proposed model is reduced to the endochronic theory of thermoplasticity. Numerical calculations demonstrate good agreement with experimental data, confirming the effectiveness and adequacy of the developed model. The proposed approaches can be utilized in the design of composite structures operating under complex thermo-mechanical conditions. Thus, the developed mathematical model enhances the predictability of the mechanical behavior of composite materials and expands their application potential in high-tech industries.

Keywords: Plasticity, thermoplasticity, endochronic theory, thermodynamics, internal state variables, kinetic relationships, composite materials, non-isothermal loading, nonlinear deformation, constitutive relations.

UDC: 539.3

Received: 10.01.2025
Revised: 17.06.2025
Accepted: 14.04.2025

DOI: 10.37972/chgpu.2025.63.1.005