L.104.22260 Simulation of materials

Instructors: Dr. Ismail Caylak; Prof. Dr. Rolf Mahnken

Event type: Lecture

Org-unit: Maschinenbau

Displayed in timetable as: MaSim

Hours per week: 2

Language of instruction: Englisch

Min. | Max. participants: - | -

Requirements and recommendations:
Basic knowledge in mechanics and mathematics, FEM 1

Aim of the event:
In most applications of materials in mechanical engineering, like elastomers or metals, the range of linear Hooke’ s law is violated, such that geometrically or physically nonlinear material behaviour has to be considered. The lecture provides basic knowledge on mathematical description of such effects and its simulation with the finite element method. Upon using modules of rheology three dimensional formulations of the constitutive equations are derived, which allow for simulation of viscoelastic and viscoplastic behavior. In addition the basic formalism of the finite element method is provided, such as variational formulation and Galerkin method, and furthermore solution techniques for solution of nonlinear discretized equations are introduced. In the exercises specific attention is paid to the use of commercial program systems for Pre- and Postprocessing. Examples of metal forming are treated.

Target group:
Students of mechanical engineering,
Techno mathematics, Physics, Informatics

Contents:
Modell equations visco elasticity

- Definition of visco elasticity ("equilibrium stress")

- Basic moduls ("Hooke"- , damping), combined module (Maxwell element)

- Three dimensional modelling (deviatoric and volumetric decomposition of stress and strain tensors)

- Options of program ABAQUS

Modell equations visco plasticity

- Definition of visco plasticity ("static yield stress")

- Basic moduls ("Hooke"- , damping, friction) combined moduls

- Three dimensional modelling (deviatoric and volumetric decomposition of stress and strain tensors)

- Options of program ABAQUS

Multi dimensional finite element Formulation

- Variation principles, Galerkin method

- Shape functions, isoparametric concept

- Solution techniques for nonlinear equations, options of program ABAQUS

Introduction to contact algorithms (optional)

Introduction to mixed FE elements (optianal)

Introduction to geometrically nonlinear problems (optional)

Applications of FEM in Pre- und Post-Processing

- Pre-processing of simple geometrical structures with ABAQUS CAE

- Visco elastic behavior of three dimensional FE-structures

- Visco plastic behavior of three dimensional FE-structures

- Variation of materials, element types, meshing

- Simulation of creep and relaxation

- Thermal- mechanical simulation of gasturbine blade

- Simulation of metal forming with large plastic deformations

- Post-Processing

Contact person:
Prof. Mahnken

Literature:
O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, 5th edition, Butterworth-Heinemann, 2000

G. A. Holzapfel, Nonlinear Solid Mechanics, John Wiley & Sons, Ltd, 2000

Supplementary events:
see catalogue for course on material science