12.7 STRAIN

Stress and strain are linearly related by Hooke's law in the elastic region of most engineering materials as discussed in Chapter 2. Strain is also a second-order tensor and can be expressed for the 3-D case as

(12.4a)

and for the 2-D case as

(12.4b)

where ? represents either a normal or a shear strain, the two being differentiated by their subscripts. We will also simplify the repeated subscripts for normal strains to ? _x, ? _y, and ? _z for convenience while retaining the dual subscripts to identify shear strains. The same symmetric relationships shown for shear stress components in equation 12.3 also apply to the strain components.