A Nonlinear Breakage Mechanics Model: From Extreme Entire Life Model to Breakage Evolution of Limestone Based on Separation of Helmholtz Free Energy under Cyclic Loading

Rock structures and load conditions play a considerable role in the deformation and failure process of rocks. To explore the nonlinear mechanical mechanism of brittle rocks, this study presents the extreme entire life constitutive equation, breakage equation, and rock resistance breakage energy (RBE) equation of limestone specimens under unequal amplitude cyclic loads. The theoretical model is based on the calculus method and thermodynamic principle, and the Helmholtz free energy of a rock system after the action of a composite system is nonlinearly separated. The extreme entire life constitutive equation of limestone is deduced on the basis of analytical solutions of nonlinear separation parameters and breakage evolution, whereas the breakage equation is deduced on the basis of the principles of residual breakage energy and thermodynamics. We present the analytical solution of the material RBE, which reflects the ability of rocks to resist breakage under load. The model performance is verified by limestone samples with different prefabricated cracks under unequal amplitude cyclic loading. This research may lay the foundation for studies of nonlinear breakage models under different conditions.