It is known that there are great types of materials, especially the geotechnical materials, e.g., rock, soil, with obvious differences in elastic modulus and Poisson’s ratio under tension and compression in nature. However, the current investigation for this type of material is still not sufficient. In this study, the elastoplastic analytical solutions of stress and displacement for the circular ring expansion problem are derived based on the SMP yield criterion and bi-modulus theory. The effect of the bi-modulus characteristics of materials on the distribution of stress, strain, and displacement, and the effect of friction angle on the critical internal pressure Pc\documentclass[12pt]{minimal}
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\begin{document}$${P}_{c}$$\end{document} and the ultimate internal pressure Pu\documentclass[12pt]{minimal}
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\begin{document}$${P}_{u}$$\end{document} in the expansive circular ring are then further investigated. It is shown by the analytical results that the distribution pattern and the magnitude of stress, strain, and displacement in the expansive circular ring, as well as the critical internal pressure Pc\documentclass[12pt]{minimal}
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\begin{document}$${P}_{c}$$\end{document}, the ultimate internal pressure Pu\documentclass[12pt]{minimal}
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\begin{document}$${P}_{u}$$\end{document} applied on the internal radius of the circular ring are all significantly affected by the modulus ratio, i.e., R=Et/Ec=νt/νc\documentclass[12pt]{minimal}
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\begin{document}$$R={E}_{t}/{E}_{c}={\nu }_{t}/{\nu }_{c}$$\end{document}. (Ec\documentclass[12pt]{minimal}
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\begin{document}$${E}_{c}$$\end{document} and Et\documentclass[12pt]{minimal}
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\begin{document}$${E}_{t}$$\end{document} are respectively the elastic modulus under compression and tension;νc\documentclass[12pt]{minimal}
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\begin{document}$${ \nu }_{c}$$\end{document} and νt\documentclass[12pt]{minimal}
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\begin{document}$${\nu }_{t}$$\end{document} are respectively the Poisson ratios under compression and tension). Based on the proposed analytical solution, the effect of the SMP yield criterion and Mohr-Coulomb yield criterion on the stress in the plastic zone in the circular ring is compared. It is found that the stress in the plastic zone in the circular ring is overestimated by the Mohr-Coulomb yield criterion.
