Damage variable based on three-dimensional measurements of crack geometry (1)
Publication Name: Strength, fracture and complexity
Continuum damage mechanics models, while elegant and useful, suffer from what are typically highly idealized relationships between model and material. In this work, using three-dimensional measurements of internal cracking, direct, albeit simple relationships were made between the quantity of cracking and a corresponding scalar damage variable. Geometric properties (surface area, volume, and fractal dimension) 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 fractal dimension of the internal crack system. 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.