Plastic limit state of the hollow sphere model with non-associated Drucker–Prager material under isotropic loading

The paper is devoted to the determination of plastic limit state of a hollow sphere with a Drucker–Prager matrix and subjected to hydrostatic loading. There are two possible plastic regimes corresponding respectively to the tensile and compressive stresses. For the associated case (dilation angle equal to the friction angle), the collapse is complete (the whole sphere is plastified) with a unique regime. For the non-associated cases, we consider weaker solutions (partial collapse and regime change). Nevertheless, we show the collapse is complete and exhibits a single regime. Consequently, the collapse stress field and the limit load do not depend on the value of the dilation angle. This theoretical result is confirmed by numerical simulations.

► Macroscopic plastic model for “Porous non-associated Drucker–Prager”-type materials.
► Impossibility of incomplete collapse and more than one plastic regime.
► Insensitivity of the limit hydrostatic pressure to the dilation angle.
► The theoretical result is confirmed by numerical simulations.