The spring semester 2021 will generally take place online. New presence elements as of April 26 will be communicated by the lecturers.

# 151-0833-00L  Principles of Nonlinear Finite-Element-Methods

 Semester Autumn Semester 2016 Lecturers N. Manopulo, B. Berisha, P. Hora Periodicity yearly recurring course Language of instruction English

 Abstract Most problems in engineering are of nonlinear nature. The nonlinearities are caused basically due to the nonlinear material behavior, contact conditions and instability of structures. The principles of the nonlinear Finite-Element-Method (FEM) will be introduced in the scope of this lecture for treating such problems. Objective The goal of the lecture is to provide the students with the fundamentals of the non linear Finite Element Method (FEM). The lecture focuses on the principles of the nonlinear Finite-Element-Method based on explicit and implicit formulations. Typical applications of the nonlinear Finite-Element-Methods are simulations of:- Crash - Collapse of structures- Materials in Biomechanics (soft materials)- General forming processes Special attention will be paid to the modeling of the nonlinear material behavior, thermo-mechanical processes and processes with large plastic deformations. The ability to independently create a virtual model which describes the complex non linear systems will be acquired through accompanying exercises. These will include the Matlab programming of important model components such as constitutive equations Content - Fundamentals of continuum mechanics to characterize large plastic deformations- Elasto-plastic material models- Updated-Lagrange (UL), Euler and combined Euler-Lagrange (ALE) approaches- FEM implementation of constitutive equations- Element formulations- Implicit and explicit FEM methods- FEM formulations of coupled thermo-mechanical problems- Modeling of tool contact and the influence of friction- Solvers and convergence- Modeling of crack propagation- Introduction of advanced FE-Methods Lecture notes yes Literature Bathe, K. J., Finite-Element-Procedures, Prentice-Hall, 1996 Prerequisites / Notice If we will have a large number of students, two dates for the exercises will be offered.