Development and verification of a methodology for Murnaghan’s defining relation сoncretization
https://doi.org/10.22405/2226-8383-2025-26-4-302-315
Abstract
In paper the methodology of concretization of five-constant Murnaghan’s defining relation is described, using the problem of homogeneous uniaxial tension (compression) of a sample
made of a nonlinear elastic material. The methodology is based on the use of experimentally observed values of axial load and transverse elongation of a prismatic sample as a function
of its axial elongation. The experimental curves are approximated by theoretical dependences following from the solution of the tensile-compression problem within the framework of the
considered constitutive relation. Material constants are determined from the requirement of minimal differences between experimental and theoretical data using the least squares method. Аn automated numerical experiment using the python programming language is described. The collected data was used to demonstrate the performance of the proposed concretization of Murnaghan’s defining relation. The numerical experiment was carried out in the local strength analysis package CAE Fidesys. The correctness of the proposed methodology was verified by comparing experimental data and theoretical data obtained for material constants determined within the framework of the presented algorithms for the concretization of the Murnaghan’s defining relation.
About the Authors
Victor Vyacheslavovich Kozlov
Tula State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Alexandra Vyacheslavovna Filatova
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
master of sciences, research laboratory assistant
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Review
For citations:
Kozlov V.V., Filatova A.V. Development and verification of a methodology for Murnaghan’s defining relation сoncretization. Chebyshevskii Sbornik. 2025;26(4):302-315. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-302-315
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