Determine the most general form of A(N) with the property that it is invariant (i.e unchanged) when N ?

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Determine the most general form of A(N) with the property that it is invariant (i.e unchanged) when N ?

Consider the form taken by the stress versus rate-of-strain relation. In particular, if we seek a linear relation between t and ?u, then we have seen in lecture that t = A : ?u or tij = Aijkl ?uk ?xl , (70) where now A depends on N as well, i.e. A(N). Assume that there are no applied external fields so that t is symmetric. Also, assume that (70) only depends on E. (a) Determine the most general form of A(N) with the property that it is invariant (i.e unchanged) when N ? -N. Hint: The components Aijkl involve of the identity tensor, N, and their products, which satisfy the symmetries required

 

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