Toward a Physical Damage Variable for Concrete

Continuum damage mechanics models, while elegant and useful, suffer from what are typically highly idealized relationships between model and material. In this technical note, using three-dimensional (3D) measurements of internal cracking, direct, albeit simple relationships were made between the quantity of cracking and a corresponding scalar damage variable. Geometric properties of internal cracks were measured through 3D image analysis of in situ microtomographic scans of small concrete specimens subject to compression. A scalar damage variable was determined from the changes in stiffness measured in successive loading cycles. Results showed a nearly linear relationship between the damage variable and the volume of new cracks formed. In contrast, results showed a nonlinear relationship between the damage variable and the crack surface area. Such relationships can potentially lead to a more physical basis for continuum damage formulations.