Course detail

# Nonlinear Mechanics and FEM

The course is a follow-up to basic lectures in solid mechanics, which are traditionally limited to linear problems, and introduces the basic nonlinearities. Material nonlinearity is represented by several models of plastic behaviour, viscoelasticity and hyperelasticity.
Next, contact problems, stability, large displacement and large strain problems are presented. Although some classical solutions to selected nonlinear problems are mentioned (Hertz contact, deformation theory of plasticity),
attention is given to numerical solution. Above all, the relation between stability and convergence of numerical solution and physical interpretation of the analysed problem is thoroughly inspected. In the second part, students work on individual projects under the guidance of tutor.

Learning outcomes of the course unit

Students learn how to solve basic types of nonlinear behaviour in solid mechanics. They can prepare numerical computational model, solve it using some of the commercial FE systems and make a rational analysis of typical problems connected to the PhD dissertation topic.

Prerequisites

Mathematics: linear algebra, matrix notation, functions of one and more variables, calculus, ordinary and partial differential equations. Others: basic theory of elasticity, theory and practical knowledge of the FEM.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

T.Belytschko, T.Liu, K.Moran: Nonlinear Finite Elements for Continua and Structures. J.Wiley, New York, 2000 (EN)
M.Okrouhlík, editor: Mechanika poddajných těles, numerická matematika a superpočítače. Ústav termomechaniky AV ČR, Praha, 1997
G.A.Holzapfel: Nonlinear Solid Mechanics, Wiley, 2000 (EN)
C.Höschl_: Kontaktní úlohy a lisované spoje. Dům techniky ČSVTS Praha, 1985
M.A.Crisfield: Non-linear Finite Element Analysis of Solids and Structures 1-2, Wiley, 1991-97 (EN)

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline.

Assesment methods and criteria linked to learning outcomes

Final evaluation is based on the ability of active work with a selected FEM system, which is proved by individual preparation and presentation of a semestral project.

Language of instruction

Czech, English

Work placements

Not applicable.

Aims

The aim of the course is to provide students with advanced knowledge and experience with the solution of nonlinear problems of solid mechanics, connected with the topic of PhD dissertation.

Specification of controlled education, way of implementation and compensation for absences

Active participation in the course is controlled individually according to the progression of the semestral project.

Classification of course in study plans

• Programme D-APM-K Doctoral, 1. year of study, summer semester, 0 credits, recommended
• Programme D-IME-P Doctoral, 1. year of study, summer semester, 0 credits, recommended

• Programme D4P-P Doctoral

branch D-APM , 1. year of study, summer semester, 0 credits, recommended

#### Type of course unit

Lecture

20 hours, optionally

Teacher / Lecturer

Syllabus

1. Introduction to numerical solution of nonlinear problems of solid mechanics
2. Material nonlinearity
3. Stability of structures, bifurcation, buckling
4. Large deformation
5. Contact problems
6. Simulation of material damage, ductile fracture, fracture mechanics
7. Explicit solvers, solution stability, mesh-dependent solutions
8.-12. Solution of individual projects, consultations
13. Presentation of individual projects

eLearning

eLearning: opened course