Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to self-learn continuum mechanics, and I have a question regarding the development of the deformation gradient (which ultimately leads to green's deformation tensor).

I have attached the specifics of the question in a attached photo.

Ultimately, there comes a point when determining the deformation using the change in magnitude of the square of dX and dx:

dx^2 - dX^2 = dxidxi-dXadXa

However, somehow using a previous equation (dxi = xi,adXa) and the susbtitution property of the kronecker delta, they come up with:

dx^2 - dX^2 = xi,adXa*xi,bdXb - delta(ab)*dXa*dXb

My question is - how was the kronecker delta substituted in? There is no direction associated with magnitudes. Further - where did the subscript "B" come from and what does it represent physically?

Any help would be greatly appreciated.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Continuum Mechanics - Deformation gradient

Loading...

Similar Threads for Continuum Mechanics Deformation | Date |
---|---|

B Series expansion of velocities | Apr 1, 2017 |

I How do we compute an integral with a dot product inside ? | Dec 30, 2016 |

B A simple differentiation and partial differentiation | Apr 24, 2016 |

Integration and continuum | Aug 10, 2014 |

Integrals and continuum vs discrete | Jun 4, 2010 |

**Physics Forums - The Fusion of Science and Community**