Exact solutions for the linear hardening elastoplastic model in functionally graded spherical shell

• The elastoplastic linear hardening model for FGMs spherical shell is studied analytically. • Exact solutions of displacement and stress in different deformation states is obtained. • The exact solutions of critical loads between four different deformation states are given. • The effect of internal pressure and FGMs parameters on the elastoplastic state is reported. As functionally graded materials (FGMs) technology advances, there has been a growing emphasis on the mechanical analysis of FGMs structures. Exceeding the yield strength in FGMs structures often leads to irreversible plastic deformation in localized regions under applied loads. An analysis of the linear hardening elastoplastic model is necessary to assess accurately the load-carrying capacity of these structures. It is assumed that the elastic modulus of FGMs spherical shell varies with the thickness distribution of the structure according to a power function. This paper provides the exact solutions for the linear hardening elastoplastic model in the FGMs spherical shell under mechanical loads, including purely elastic, partially plastic, and fully plastic deformation states. The elastoplastic theory is employed to analyze the linear hardening elastoplastic model, and each deformation state is thoroughly analyzed. A significant contribution of this research is the presentation of comprehensive exact solutions for the linear hardening elastoplastic model in FGMs spherical shell, addressing all deformation regions. The findings demonstrate that the radial variation in material properties significantly influences the elastoplastic model analysis of the FGMs spherical shell. These conclusions are expected to aid in the design of FGMs spherical shells to mitigate yielding under high circumferential stress.