| This course prepares for performing nonlinear finite element analysis with large deformation elastic and plastic material models. Nonlinear behaviour can be triggered by nonlinear stress-strain relations of the material, like in rubber or plastic deformation of metals, or by nonlinear displacement-strain relations when deformations or rotations are large. |
In the mechanics of large deformations, new definitions for stress and strain will be introduced (the classical strain definition is not valid for large deformations). Large deformations almost always lead to nonlinear stress–strain relations. Attention will be given to mathematically correct kinematical relations. The transformation from the undeformed to the deformed state is described with the deformation gradient tensor. Strain measures are defined in a Eulerian and a Lagrangian frame. Strain-rate definitions are based on the velocity gradient and relations with the total strain measures are derived. Special attention is given to objectivity of these relations.
The stress in a material is defined based on the total strain or based on strain-rate relations. For this course, a short overview of applicable vector and tensor equations is provided. For rubber-like materials, hyperelastic models are introduced with special attention to nearly-incompressible models. The focus will be on models based on invariants of the stretch tensor, like the neo-Hookean model and the Mooney–Rivlin model. For metal plasticity, elastoplastic models are introduced, as well as the numerical algorithms to implement them in a finite element code. Isotropic and anisotropic yield functions are introduced for use in bulk forming and in sheet metal forming simulations (Tresca, Von Mises and Hill). Work hardening models based on isotropic and kinematic hardening theories are introduced with commonly used hardening relations (Swift and Voce). An instability criterion and fracture criterion is introduced for use in simulations of sheet forming processes. Finally, continuum damage models are considered to model failure of the material.
The course comes with a practical assignment to design and simulate forming of a real product using a commonly used commercial software program (Abaqus). This assignment will provide further insight in the plastic behaviour of metal during a specific forming process (deep drawing).
Why this course: Although most structures are designed to operate in the linear regime, nonlinear behaviour is essential in a number of applications. This is the case e.g. in forming processes, where material is permanently deformed into a desired shape or in the case where large deformations of components determine the performance, as in rubber seals. Another application of nonlinear analysis is to determine the safety margin when structures are overloaded. Will a linearly designed structure catastrophically collapse, or can an overload be sustained at a minor loss of functionality?
Course highlights:
- Mathematically consistent formulations for strains and stresses under large deformations;
- Nonlinear models for elasticity, plasticity and damage evolution;
- Finite element modeling of a forming process;
For whom: Professionals with basic knowledge on Finite Element Method. If needed, the course on Advanced Topics in Finite Element Method at the UT can be followed as preparation for this course. Knowledge of Linear Solid Mechanics is recommended but not strictly required.
From whom: prof.dr.ir. A.H. van den Boogaard, dr. S. Perdahcioglu
Practical information: This is a regular master course, in which students as well as professionals can participate. The course combines lectures on the topics mentioned above. The lectures will be on-site, supported by recorded micro-lectures on certain topics. Practical assignments are scheduled in parallel to apply and deepen the knowledge and skills acquired. The assignments are FEM simulation problems, which the participants have to elaborate and get support and feedback on. Some self-study is required. At the end of the course, the gained knowledge and skills can be applied and checked in a written exam.
Location: University of Twente, Enschede, NL
Duration: The course is scheduled annually from April till July. It requires 140 hours of study load.
Costs: € 2067,15
More information:
Content of the course: dr. Semih Perdahcioglu, e.s.perdahcioglu@utwente.nl.
Registration: Registration form | Faculty of Engineering Technology (ET)