Hysteresis and nonlinear elasticity in rocks
The purpose of this paper is to describe a theory of the propagation of elastic waves in hysteretic nonlinear elastic materials, e.g., rock. In the next section, we introduce the Priesach-Mayergoyz (P-M) model [6,7] of hysteretic systems and adapt it to describe the hysteretic mesoscopic elastic units (HMEU) determining the elastic properties of a rock. We combine the P-M model with effective medium theory (EMT) [8] to find the elastic response of a rock that has experienced a specified pressure history. Next, we consider elastic wave propagation in a hysteretic nonlinear elastic system governed by a history dependent equation of state. We consider one-dimensional propagation of compressional waves. The equation of motion for the longitudinal displacement field contains the same hysteretic nonlinear interactions that characterize the equation of state. We solve the equation of motion using the Green function technique developed by McCall [9]. This solution lets us identify the qualitative features in harmonic generation that are signatures of nonlinearity and hysteresis.
- Research Organization:
- Los Alamos National Lab., NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 10108040
- Report Number(s):
- LA-UR--93-4143; CONF-9308167--5; ON: DE94003937
- Country of Publication:
- United States
- Language:
- English
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