Microplane Model for Progressive Fracture of Concrete and Rock

Abstract

A constitutive model for a brittle aggregate material that undergoes progressive tensile fracturing or damage is presented. It is assumed that the normal stress on a plane of any orientation within the material, called the microplane, is a function of only the normal strain on the same microplane. This strain is further assumed to be equal to the resolved component of the macroscopic strain tensor, while the stress on the microplane is not equal to the resolved component of the macroscopic stress tensor. The normal strain on a microplane may be interpreted as the sum of the elastic strain and of the opening widths (per unit length) of all microcracks of the same orientation as the microplane. An additional volumetric elastic strain is introduced to adjust the elastic Poisson ratio to a desired value. An explicit formula which expresses the tangent stiffness of the material as an integral over the surface of a unit hemisphere is derived from the principle of virtual work. The model can represent experiment...