Automatic Differentiation for Solid Mechanics in Julia | Andrea Vigliotti | JuliaCon 2022

Automatic Differentiation (AD) is widely applied in many different fields of computer science and engineering to accurately evaluate derivatives of functions expressed in a computer programming language. In this talk we illustrate the use of AD for the solution of Finite Elements (FE) problems with special emphasis on solid mechanics.

Resources

Contents
0:10 Opening and introduction
0:30 Why AD for solid Mechanics?
1:50 One example, the rod element
2:50 Why Julia?
3:24 AD4SM.jl
4:00 How a second order forward mode AD System works
6:46 Examples of simulation results

[andreavigliotti]

there is a typo in the last slide starting at 7:13. The correct equation should read

U(u, d) = \\phi^{-} + (1-d)^2\\, \\phi^{+} + \\frac{G_c}{2}\\left(d^2 + l_0^2\\, d_{, i}d_{, i}\\right)