One or more mechanical parameters of a structure subjected to a force or condition are measured using distributed, optical fiber sensing technology. At least a curved portion an optical fiber having is attached to an object. A distributed, optically-based, strain sensing technique is used to determine strain information associated with multiple points along the curved portion of the fiber. The determined strain information is processed to generate one or more representations of one or more of the following: an expansion of the object, a thermal gradient associated with the object, or a stress-induced strain at multiple locations on the object corresponding to ones of the multiple points. An output is generated corresponding to the representation.