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Tensor derivative (continuum mechanics) : ウィキペディア英語版
Tensor derivative (continuum mechanics)
The derivatives of scalars, vectors, and second-order tensors with respect to second-order tensors are of considerable use in continuum mechanics. These derivatives are used in the theories of nonlinear elasticity and plasticity, particularly in the design of algorithms for numerical simulations.〔J. C. Simo and T. J. R. Hughes, 1998, ''Computational Inelasticity'', Springer〕
The directional derivative provides a systematic way of finding these derivatives.〔J. E. Marsden and T. J. R. Hughes, 2000, ''Mathematical Foundations of Elasticity'', Dover.〕
== Derivatives with respect to vectors and second-order tensors ==
The definitions of directional derivatives for various situations are given below. It is assumed that the functions are sufficiently smooth that derivatives can be taken.

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