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LONGITUDINAL STRAIN

         There are two kinds of changes that occur as a result of natural deformation. The first which causes changes of lengths of elements is called longitudinal strain and the second which changes the orientation of various elements or objects is called the shear strain. If the original length is lo and the length after deformation ld, then extension, e, is given by 

     e=( ld-lo)/lo  :e could be negative or positive depending on whether the length is decreased or increased.   The quadratic extension, designated by  l, is given by 

     l=(ld/lo)2      which is the same as  (1+e)2     

and the reciprocal quadratic extension designated by l' is given by

    l'=(lo/ld)2  or  [(1+e)2  ]-1

 The longitudinal strain can also be expressed in natural logarithmic form as natural strain and designated by  e.

e=loge  (1+e)  or e=ln (1+e) or e=loge =  Íl