Material Nonlinearity I — Lesson 3

This lesson covers the concept of nonlinearity in finite element modeling, specifically focusing on material nonlinearity. It explains how properties such as thermal conductivity, specific heat, and viscosity can change with temperature, leading to nonlinearity. The lesson also discusses how nonlinearity can be classified into reversible and irreversible nonlinearity, with examples of each. It further delves into the strategies for handling nonlinearity in finite element-based modeling, including direct iterative techniques and the Newton-Raphson method. The lesson uses the example of steady-state heat transfer equation by conduction to illustrate these concepts.

Video Highlights

01:07 - Explanation of how the matrix itself depends on temperature and how this introduces nonlinearity into the equation
05:39 - Direct iterative technique for solving nonlinearity in finite element modeling
34:56 - Newton Raphson method
45:59 - Comparison between the direct iterative technique and the Newton Raphson method in terms of convergence speed and complexity

Key Takeaways

- Material nonlinearity signifies the variation of properties within the useful range of an application.
- Nonlinearity can be classified into reversible and irreversible nonlinearity.
- Direct iterative techniques and the Newton-Raphson method are strategies to handle nonlinearity in finite element-based modeling.
- The accuracy level of the result depends on how effectively the non-linear behavior is considered.
- The Newton-Raphson method can provide a faster convergence to the solution compared to direct iterative techniques.