Strain softening is a characteristic displayed in several materials encountered in civil engineering. For example, rock, concrete, and dense soil exhibit the behavior where the tangent modulus decreases from an initial positive value and becomes negative as strain increases. When softening is involved with a structural component, however, an internal snap-back instability may occur, with the softening branch taking on a positive slope. Failures of this type would be catastrophic even in a displacement-controlled setting and must be prevented. The objective of this research is to develop and apply a theory of brittleness in order to predict the global behavior of a structure composed of a strain-softening material. An elastic-plastic constitutive law will be adoptive for the local strain components, while the softening behavior will be described in terms of displacement components through a cohesive-zone model of fracture. Experiments will be conducted in a closed-loop, servo-hydraulic testing system to capture the post-failure regime and to evaluate the necessary material parameters. The softening response of concrete beams in three-point bending will be studied by varying the geometry, size, and constraint, while recording the acoustic emissions from the failure process. Acoustic emission testing in proposed as a viable nondestructive technique to detect the onset of an instability. This research will provide an analytical explanation and present experimental evidence of the snap-through versus snap-back behavior of strain-softening beams.
