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When forces are applied to a body, deformation, the change in length or shape, occurs. The change in length, divided by the original length, is the strain. We use strain to normalize deformations with respect to the size of the geometry.
Relative change in length of a line element oriented in arbitrary direction \( n \).
Length change divided by total length.
Change in angle between line segments oriented in perpendicular directions \( n \) and \( t \):
When strains are small, the small angle approximation, \( \sin(\theta)\approx \theta \), results in
The components of normal and shear strain can be combined into the strain tensor. This is a symmetric matrix.
The first subscript describes the surface orientation in the normal direction. The second subscript describes the direction of the stress.
Heads up!
Similar to stress tensor, strain tensor also builds on this content later in the course.
Learn more about this topic on the Stress Transformation page.
Initial and final lengths of some section of the specimen are measured, perhaps by some handheld device such as a ruler. Axial strain computed directly by following formula:
A clip-on device that can measure very small deformations. Two clips attach to a specimen before testing. The clips are attached to a transducer body. The transducer outputs a voltage. Changes in voltage output are converted to strain.
Small electrical resistors whose resistance charges with strain. Change in resistance can be converted to strain measurement. Often sold as "rosettes", which can measure normal strain in two or more directions. Can be bonded to test specimen.
A calibrated wire is set into vibration and its frequency is measured. Small changes in the length of the wire as a result of strain produce a measurable change in frequency, allowing for accurate strain measurements over relatively long gauge lengths.
Image placed on surface of test specimen. Image may consist of speckles or some regular pattern. Deformation of image tracked by digital camera. Image analysis used to determine multiple strain component.