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.[1]
The directional derivative provides a systematic way of finding these derivatives.[2]
- ^ Simo, J. C.; Hughes, T. J. R. (1998). Computational Inelasticity. Springer. doi:10.1007/b98904. ISBN 978-0-387-97520-7.
- ^ Marsden, Jerrold E.; Hughes, Thomas J. R. (2000). Mathematical Foundations of Elasticity. Dover. ISBN 978-0-486-678658.
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