Damage variables based on three-dimensional measurements of crack geometry

Issue title: 11th International Conference on Fracture (ICF11), Torino, Italy, 20–25 March 2005. Mini-Symposium – “Complexity, Scaling and Non-linearity in the Mechanics of Advanced Materials”

Article type: Research Article

Authors: Landis, Eric N.

Affiliations: University of Maine, Department of Civil and Environmental Engineering, 5711 Boardman Hall, Orono, ME 04469, USA Tel.: +1 207 581 2173; Fax: +1 207 581 3888; E-mail: landis@maine.edu

Abstract: 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.

Journal: Strength, Fracture and Complexity, vol. 3, no. 2-4, pp. 163-173, 2005