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    Analysis of the compressible, isotropic, neo-Hookean hyperelastic model
    (Dordrecht [u.a.] : Springer Science + Business Media B.V, 2023) Kossa, Attila; Valentine, Megan T.; McMeeking, Robert M.
    The most widely-used representation of the compressible, isotropic, neo-Hookean hyperelastic model is considered in this paper. The version under investigation is that which is implemented in the commercial finite element software ABAQUS, ANSYS and COMSOL. Transverse stretch solutions are obtained for the following homogeneous deformations: uniaxial loading, equibiaxial loading in plane stress, and uniaxial loading in plane strain. The ground-state Poisson’s ratio is used to parameterize the constitutive model, and stress solutions are computed numerically for the physically permitted range of its values. Despite its broad application to a number of engineering problems, the physical limitations of the model, particularly in the small to moderate stretch regimes, are not explored. In this work, we describe and analyze results and make some critical observations, underlining the model’s advantages and limitations. For example, a snap-back feature of the transverse stretch is identified in uniaxial compression, a physically undesirable behavior unless validated by experimental data. The domain of this non-unique solution is determined in terms of the ground-state Poisson’s ratio and the state of stretch and stress. The analyses we perform are essential to enable the understanding of the characteristics of the standard, compressible, isotropic, neo-Hookean model used in ABAQUS, ANSYS and COMSOL. In addition, our results provide a framework for the parameter-fitting procedure needed to characterize this standard, compressible, isotropic neo-Hookean model in terms of experimental data.
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    Investigation of constitutive relationship and dynamic recrystallization behavior of 22MnB5 during hot deformation
    (Amsterdam : Elsevier B.V., 2019) Xu, Y.; Birnbaum, P.; Pilz, S.; Zhuang, X.; Zhao, Z.; Kräusel, V.
    In order to analyze the softening behavior of 22MnB5 steel and further predict the constitutive relationship during hot sheet metal forming, a series of isothermal hot compression tests were conducted at the temperature range of 800–950 °C and strain rate range of 0.01–0.8 s−1 on BAEHR 805 A/D thermo-mechanical simulator system. Based on the friction corrected flow curves, the characteristic strain and stress of dynamic recrystallization (DRX) were derived from the Kocks-Mecking plots and expressed as a function of Zener-Hollomon parameter. Moreover, a physical constitutive model considering work hardening (WH), dynamic recovery (DRV) and DRX as well as corresponding JMAK-type DRX kinetics were developed. The results showed that the established physical equations can accurately predict the flow behavior with a correlation coefficient of 0.997 and average absolute relative error of 3.89%. Optical observation of the microstructure after hot compression revealed that the established DRX kinetics accurately reflects the reality, and then a Zener-Hollomon parameter dependent dynamic recrystallized grain size model was developed. Furthermore, EBSD analysis was carried out to study the effect of deformation conditions on martensite morphology and the results show that a lower temperature and higher strain rate lead to a finer martensite packet while the martensite block width becomes larger under the higher strain rate.