A refined method for determining rheological parameters of the maxwell-gurevich equation from polymer relaxation curves using the example of epoxy resin edt-10

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https://doi.org/10.58224/2618-7183-2026-9-3-5
This paper presents a refined methodology for determining the rheological parameters of the nonlinear generalized Maxwell-Gurevich equation, which is widely used to describe creep and relaxation processes in polymer materials. Despite the extensive application of this constitutive model in polymer mechanics, existing methods for identifying its key parameters – namely the high-elasticity modulus E∞, the rate modulus mcr, and the initial relaxation viscosity ηcr,0 – often yield approximate values that do not fully capture the material's behavior across different deformation levels. The proposed approach addresses this limitation through a comprehensive two-stage algorithm based on the processing of stress relaxation curves at various initial strain levels. In the first stage, preliminary parameter values are obtained using an analytical approximation method that involves polynomial fitting of creep strain data and logarithmic transformation of the relaxation viscosity coefficient. The second stage employs numerical optimization techniques implemented in the Python programming language, specifically the scipy.optimize.fmin function for global minimum search, combined with the fourth-order Runge–Kutta method for solving the differential equation of creep strain rate. The methodology was validated using experimental data for EDT-10 epoxy resin – a thermosetting polymer widely employed in structural applications – tested at 20°C under six different initial relative deformations ranging from 0.008 to 0.035. The relaxation curves were digitized from classical literature sources and processed according to the developed algorithm. The results demonstrate that the rheological parameters of the Maxwell-Gurevich equation exhibit significant dependence on the initial strain (stress) level, contrary to the common assumption of their constancy for a given temperature. Specifically, the high-elasticity modulus E∞ decreases nonlinearly from 19142.71 MPa to 2643.07 MPa as the initial deformation increases, while the rate modulus mcr shows an increasing trend from 3.58 MPa to 22.48 MPa. The initial relaxation viscosity ηcr,0 decreases by approximately two orders of magnitude, from 8.14•10⁵ MPa•h to 1.33•10⁴ MPa•h. Functional relationships approximating these dependencies as functions of the initial elastic strain were established with high correlation coefficients (R² ranging from 0.9776 to 0.9988 for individual curves). A comparative analysis was conducted with three previously published parameter sets for EDT-10 epoxy resin. The comparison reveals that traditional constant-parameter approaches significantly underestimate the high-elasticity modulus and lead to excessively rapid stress relaxation, particularly at higher initial strain levels (>0.0155), where the solution degenerates. In contrast, the proposed strain-dependent parameterization yields theoretical relaxation curves that closely match the experimental data across the entire range of deformations, with coefficients of determination R² exceeding 0.97 for all curves except the lowest strain level (0.008), where digitization errors are more pronounced. The methodology demonstrates robustness and can be extended to other polymer materials and loading conditions, including creep tests where the stress remains constant. The findings have important implications for the mechanics of polymer structures, adhesive joints, and composite materials, where accurate prediction of long-term deformation behavior under various stress states is essential for reliable design and service life assessment. Future research directions include validation of the proposed hypothesis for creep curves and investigation of temperature-dependent parameter variations.
Keywords:
Maxwell-Gurevich equation, rheological parameters, relaxation curves, epoxy resin EDT-10, nonlinear viscoelasticity, numerical optimization, polymer mechanics, parameter identification, Python
Litvinov S.V.
Candidate of Technical Sciences, Associate Professor of Construction Mechanics and Theory of Structures Department, Don State Technical University
Yazyev B.M.
Doctor of Technical Sciences, Professor of Construction Mechanics and Theory of Structures Department, Don State Technical University
Volosatova T.A.
Candidate of Physical and Mathematical Sciences (Ph.D.), Associate Professor of Higher Mathematics Department, Don State Technical University
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Litvinov S.V., Yazyev B.M., Volosatova T.A. A refined method for determining rheological parameters of the maxwell-gurevich equation from polymer relaxation curves using the example of epoxy resin edt-10. Construction Materials and Products. 2026. 9 (3). 5. https://doi.org/10.58224/2618-7183-2026-9-3-5