
How can we determine the direction of the strains?

In this question, it is assumed that state of stress is not given for a material.
We can not measure state of stress in material under loading. We can measure strain. Even on top of that, we can only measure strain on surface of a material. there are many methods to measure strain. simplest is to draw a line on the surface and measure the length of the line after deformation. However, this method only gives average value of strain in deformation.
More accurate and widely used method is by electrical strain gauges. A single strain gauge can measure strain only one direction, not in the perpendicular of a strain gauge or shear of plane. So, more than one strain gauge is required to completely measure the state of strain. To get two-dimensional state of strain we need three values, two linear strains in perpendicular direction and shear strain. We need to obtain measurements from three strain gages. These three gages must be arranged at different orientations on the surface to form a strain Rossett. A typical example of strain rosette is shown in fig.
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