A microscopic model for stress-strain relations in rock—Part I. Equilibrium equations

Abstract

The classical microscopic model for elastic solids, based upon bonds between atoms or molecules, is modified to include more general networks and breakage of over-extended bonds. The resulting macroscopic stress-strain relation is non-linear and history dependent. The equilibrium differential equations have multiple solutions. For monotonically increasing compressive stress, it is argued that the physically appropriate solution minimizes a free energy functional. Discontinuous transition between states with different degrees of internal bond breakage can occur. Multiphase mixtures of homogeneous internal states can also occur. Various configurations of broken bonds can be interpreted as cracks.