A constitutive relationship for mechanical hysteresis of sandstone materials

Experimental results concerning mechanical hysteresis in sandstone samples, which were obtained by means of either dynamic acousto-elastic or quasi-static techniques, are mathematically modelled assuming that the critical stress at which hysteresis is activated is not an intrinsic material property, but decreases with increasing stress rate. A macroscopic strain–stress constitutive relationship is derived from this assumption, which leads the main features characterizing mechanical hysteresis in sandstones to be recovered, at least in a qualitative sense. In particular, for sinusoidal loading used in dynamic acousto-elastic experiments, the model predicts a vanishing anelastic strain and a continuous variation of the modulus defect during the entire loading cycle. Furthermore, hysteresis is shown to disappear when the frequency of the excitation approaches the static limit. Experimental results and theoretical models concerning other Earth materials and metal alloys are also considered. Although in some case, the latter results have been acquired under dramatically different experimental conditions, they are better understood, and, for this reason, are used as reference to discuss those obtained by exploiting acousto-elasticity of sandstones. The striking difference between reference findings and results in sandstone suggests that equally strikingly different mechanisms are responsible for hysteresis in the latter material system.