A continuum theory for solids containing microdefects

Abstract The conventional continuum theory is based on the constitutive equations that prescribe relations between the average stress and strain, valid when the local deformation is more or less uniform. However, when the deformation is localized, the effects of interaction among microdefects become important, and must be included in the formulation of any effective continuum theory. One promising way of establishing a continuum theory that can capture localization phenomena, is to use micromechanics. In this study, we establish a micromechanics-based continuum theory (named interaction field theory) which can model localization phenomena, such as shear failure in rocks or shear band formation in sands under compression. A new field variable (interaction field) that characterizes the effects of interaction among microdefects is introduced, and its governing integral equation is formulated. Although the technique is applicable to any material with any microstructure, for an illustration the theory is formulated and used to study the behavior of rocks under compression. Numerical results are given that illustrate the difference between the proposed theory and the conventional continuum damage mechanics. It is confirmed that the proposed theory can describe the localization process by microcracking in shear failure and axial splitting of rocks under compression.

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