The exact derivative of the exponential of an unsymmetric tensor

An exact series representation for the derivative of the exponential of a generic unsymmetric tensor is derived. The computer implementation of the derived formula is straightforward and allows the computation of the derivative of the tensor exponential to any desired degree of accuracy. In practice, the accuracy of the computed derivatives will be limited by machine precision. The application of the proposed formula to the numerical treatment of anisotropic rate-dependent and rate-independent finite single crystal plasticity is outlined.

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