<p>The stress-dilatancy relationship is fundamentally linked to the laws of thermodynamic. Most existing stress-dilatancy energy equations are based on the hypothesis that the plastic input work is equal to the frictional dissipation energy. With the concept of frozen free energy, stress-dilatancy equations with frictional dissipation as the only contribution to plastic deformation are incomplete, it is necessary to include the term of Helmholtz free energy. In this study, the irreversible composition of free energy stored within granular assembly is investigated based on the DEM results of biaxial loading and reverse loading. The results show that a fraction of the free energy stored during the biaxial loading is non-releasable when the specimen goes back to the initial stress level along the reverse loading. While only part of the released free energy during the reverse loading is used for macroscopically reversible boundary work, and the other part is dissipated by friction. By dividing the free energy into three components, the non-releasable component and the releasable component for plastic dissipation consist of the irreversible free energy which contributes to macroscopic irreversible deformation. Then, a stress-dilatancy equation is proposed by modifying the frictional dissipation energy function and establishing the irreversible free energy function. Compared with the experimental results of Ottawa and Silica sands, the proposed energy equation can well describe the macroscopic stress-dilatancy relationship of granular materials, and in particular capture the patterns of back-hook after peak point for dense materials.</p>