Nonlinear Computational Mechanics

Teaching aims

The students know fundamental principles in continuum mechanics and material modeling and are able to command the respective mathematical knowledge. They have the ability to differentiate material categories with respect to their phenomenological properties. They comprehend the fundamental of materials and are able to formulate the necessary equations for the material description.

The students have the ability to apply material knowledge to engineering problems, especially for stress analysis and structural evaluation. They have gained experience with the potential and the limits of materials and are able to select adequate material models due to their phenomenological properties on their own. The students are acquainted with the formulation of essential principles in material theory and they have improved their ability to investigate and discuss complex and interdisciplinary problems.

The students have a solid comprehension of nonlinear phenomena in structural mechanics and are experienced with the concepts for their mathematical description. They possess a theoretical understanding of the differences in the theories and the necessities and limits of their application to engineering problems.

The students gained experience with the formulation of simple elements for nonlinear phenomena. They are able to recognize the reasons for convergence problems in their context and are able to identify possible ways to overcome them.

The students are able to transfer the mathematical concepts to engineering problems. They have the ability to solve problems in this field, including correct modeling, selection of appropriate Finite Elements, contact algorithms and solution techniques, checking and discussion of results. They are able to command the mathematical and technological knowledge to investigate complex problems.

Content

Part I: Materials and Material Models

• Rheology
• Nonlinear elastic materials
• Elastic-plastic materials
• Viscous materials
• Cellular materials
• Composites

Part II: Geometrical Nonlinear and Contact Analysis

• Conservation laws in continuum mechanics
• Large deformations
• Large strains
• Combination with nonlinear material models
• Theory of stability
• Contact analysis
• Numerical solution procedures

Lecturers

• Prof. Dr.-Ing. Wellnitz, Ingolstadt University of Applied Sciences
• Prof. Dr.-Ing. Fritsch, Munich University of Applied Sciences
• Prof. Dr.-Ing. Rust, University of Applied Sciences and Arts in Hannover

Taught as

Class, practical exercise, lab exercise

Contact hours

70 hours

Examination

Written exam

ECTS

7 credits