A bipotential-based macroscopic fatigue criterion of porous materials with a pressure-sensitive and non-associated plastic solid matrix and comparison with numerical simulation

The formulation of macroscopic strength criteria under cyclic loading of ductile porous media containing a pressure sensitive and non-associated plastic matrix is still a pending issue. In this paper, a new approach is developed by using the bipotential theory. In this framework, non Generalized Standard Materials (GSM) are transformed into a class of Implicit Standard Materials (ISM), allowing the recovery of the flow rule normality in a weak form of an implicit relation. The classical shakedown theorems are extended to the homogenization of ISM. The solution of a thick wall tube under uniform pressure is established with the assumption of vanishing plastic strain increment over a single stabilized cycle. A macroscopic fatigue criterion is further delivered for the first time for porous materials with a non-associated Drucker-Prager type solid matrix. It is now possible to separate the effects of frictional and dilatancy angles. It is found that the shakedown limit load under hydrostatic loading is only related to the friction angle, but not the dilatancy one. The safety domain defined by the established criterion under general cyclic loads is comparatively reduced with the decrease of dilatancy angle. The new criterion is fully assessed by comparing the theoretical predictions to FEM-based step-by -step simulations for different values of porosity and frictional and dilatancy angles. Finally, the new criterion can also be applied to associated solid matrix as a special case and it significantly improves the accuracy of predictions provided by previous works based on the Melan's static theorem.

Automated summary

This paper presents a new method for formulating macroscopic strength criteria under cyclic loading of ductile porous media, utilizing the bipotential theory for transformation of Generalized Standard Materials (GSM) to Implicit Standard Materials (ISM). The establishment of a macroscopic fatigue criterion allows for separation of the effects of frictional and dilatancy angles, while also revealing the relationship between the shakedown limit load under hydrostatic loading and the dilatancy angle. The new criterion is validated through comparison with FEM-based simulations and shows improved accuracy compared to previous works based on Melan's static theorem.