Summary.
A stress is considered conjugate to a strain if the product of the stress and an objective rate of the strain has a trace which is equal to the rate of work per unit volume. Using Kronecker product relations, apparently new expressions for stresses conjugate to the Finger strain B, the Euler strain ∃, the Eulerian (right) stretch tensor V, and log(V) are determined. In addition, a nonclassical strain p is introduced which permits a constitutive equation expressing its Truesdell rate in terms of B and the Truesdell rate of the Cauchy stress.
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We regard a tensor as a strain if (a) it is not affected by rigid body motion and (b) its current value, given suitable compatibility conditions, determines the current displacement field to within a rigid body translation and rotation. By these criteria e is not strictly a strain and instead we later refer to it as a pseudostrain.
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Nicholson, D. On stresses conjugate to Eulerian strains. Acta Mechanica 165, 87–98 (2003). https://doi.org/10.1007/s00707-003-0037-2
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DOI: https://doi.org/10.1007/s00707-003-0037-2