Page 151 - Introduction to Continuum Mechanics
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136 Lagrangian Strain Tensor
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Thus, As = AS V i + k , this result is the same as that of (b). We note that if k is small then
As = AS to the first order of k.
Example 3.24.2
Consider the displacement components corresponding to a uniaxial strain field:
(a) Calculate both the finite Lagrangian strain tensor E* and the infinitesimal strain tensor E,
(b) Use the finite strain tensor E\i and the infinitesimal strain tensor EH to calculate — for
iiO
the element AX = ASe^.
A C A
(c) For an element AX = —/—(ej + e 2), calculate -rr from both the finite strain tensor E* and
V2 Ai
the infinitesimal strain tensor E.
Solution, (a)
Thus, the infinitesimal strain tensor gives
