3.5 Permanent deformation: Elasto-plasticity

Most rocks will exhibit permanent (plastic) deformation when loaded at large strains $\varepsilon \gtrsim 0.001$. Plastic deformation includes plastic compression strains and plastic shear strains. The theory of elasto-plasticity is covered in the Advanced Geomechanics course https://www.youtube.com/playlist?list=PLv0npDbE5HXssC2CwCAssJs0fTkKquQFj. Figure 3.23 shows an example of permanent deformation during a typical deviatoric loading test to measure Young's modulus. First-time loading usually involves plastic deformation and creep. Therefore the loading Young's modulus $E_{load}$ results smaller than the unloading modulus $E_{unload}$. While $E_{load}$ calculation lumps elastic, plastic, and creep strains, $E_{unload}$ involves mostly elastic strains. Notice the the re-loading modulus is similar to the unloading modulus $E_{unload} \sim E_{unload}$ because a re-loading path is not a first-time loading.

Figure 3.23: Loading and unloading stress paths for a shale sample. Two unloading-reloading paths were performed before rock failure. Notice that $E_{load} < E_{unload}$ because of plastic and creep strains.