MATHEMATICAL MODELING OF THE STRESS–STRAIN STATE OF AN ISOTROPIC ELASTIC BODY UNDER UNIAXIAL TENSION
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Abstract
Abstract. This paper develops a mathematical model for the uniaxial tension of a homogeneous, isotropic, linearly elastic bar. Using equilibrium, the kinematic relation, and Hooke’s law, expressions for normal stress and axial strain are derived. An analytical solution for a bar with constant cross-sectional area is presented together with an illustrative numerical calculation and a parameter study showing how load, cross-sectional area, and Young’s modulus affect elongation. The results are theoretical and are not presented as experimental measurements.
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References
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