Hysteretic nonlinear elasticity of Berea sandstone at low-vibrational strain revealed by dynamic acousto-elastic testing

Through changes in wave speed of ultrasonic pulses traversing the sample, we measure variations in the elasticity of dry Berea sandstone as a function of the applied low‐frequency (LF) axial strain (varied from 10−7 to 10−5). The approach, termed dynamic acousto‐elasticity, is the dynamic analog of static acousto‐elasticity where the wave speed is measured as a function of the applied static load. Dynamic acousto‐elasticity uses low‐frequency vibrational loading of smaller strain amplitude, typically below 10−4, and it includes inertial effects. At strain amplitudes around 10−6, compression and tension produce a material softening of the material. In contrast, a quasi‐static compression inducing a strain between 10−4 and 10−3 leads to a material stiffening. At 10−5 strain amplitude, elaborate hysteretic signatures of modulus strain are observed. The measurements provide the first direct experimental evidence of hysteretic nonlinear (wave amplitude dependent) elasticity in a sandstone at low dynamic strains. Key Points Each wave amplitude brings the material to a different metastable state First direct evidence of dynamic hysteretic nonlinear elasticity at low strain Nonlinear elastic parameters and hysteresis are wave amplitude dependent