Page 149 - Introduction to Continuum Mechanics

134 Lagrangian Strain Tensor

3.24 Lagrangian Strain Tensor

.Let

where C is the right Cauchy-Green deformation tensor and I is the identity tensor. The tensor
E* is known as the Lagrangian Finite Strain tensor. We note that if there is no deformation,
C = I and E* = 0.
From Eq. (3.23.4), we have

i.e.,

For a material element dX = dS*i, deforming into dx = dsn, where n is a unit vector, Eq.
(3.24.2) gives

Thus,

Similarly,

We note that for infinitesimal deformations, Eqs.(3.24.3) reduces to Eq. (3.8.1)
By considering two material elements dX^ = dS^i and dX^ - dS^i deforming into
n
far ' ~ ds-^m and dr ' = <&2 , where m and n are unit vectors, then Eq(3.25.2) gives

We note that for infinitesimal deformations, Eq. (3.24,4) reduces to Eq. (3.8.2).