Non-Linear Mechanics for Finite Element Analysis
| Keywords |
| Classification |
Keyword |
| OFICIAL |
Mechanical Engineering |
Instance: 2023/2024 - 2S 
Cycles of Study/Courses
| Acronym |
No. of Students |
Study Plan |
Curricular Years |
Credits UCN |
Credits ECTS |
Contact hours |
Total Time |
| PRODEM |
1 |
Syllabus since 2009/10 |
1 |
- |
6 |
28 |
162 |
Teaching Staff - Responsibilities
Teaching language
Suitable for English-speaking students
Objectives
To present nonlinear continuum mechanics, the associated finite element
formulations and the solution techniques with a unified treatment.
In the first part of the course, finite deformation in continuum mechanics and
nonlinear material behaviour is reviewed and extended. The second part of the
course is dedicated both to the finite element formulation and implementation
of the non linear (incremental) boundary value problem for different inelastic
material models.
An understanding of the computational tool being used, be it a
calculator or a computer.
An understanding of the problem to be solved.
The construction of an algorithm which will solve the given physical
problem to a given desired accuracy and within the limits of the
resources (time, memory, etc) that are available.
Learning outcomes and competences
An understanding of the computational tool being used, be it a
calculator or a computer.
An understanding of the problem to be solved.
The construction of an algorithm which will solve the given physical
problem to a given desired accuracy and within the limits of the
resources (time, memory, etc) that are available.
Working method
Presencial
Program
1. Tensors: Algebra, Linear Operators, Calculus
2. Differentiation
3. Kinematics: Motion, Grad, Polar Decomp.;Strain, Rates
5. Global Balance: Mass, Momentum, Energy, Entropy
6. Stress: Cauchy’s Theorem and Alt. Measures
7. Mech. Boundary Value Problem
8. Invariance: Observer
9. Fe Form. Derivation of a Non-linear FE Method Iterative Solution of a Non-linear Equation System - NR Method. Computation of The Tangential Stiffness Matrix; Alternative Representation of The Tangent Tensor
10. Finite Elasticity:Frame-indifference, Isotropy;Hyperelasticity: Neo-hooke Material Model, Ogden Material Model;Computation of the Tangent Tensor
11. Rheological models (viscoelasticity, ..)
12. Continuum mechanical formulation:Viscoelasticity;Damage
13. FE implementation: Vector of Internal Forces and Tangential stiffness matrix; Computation of evolution equations and consistent material tangen; Rate-independent material behaviour
Mandatory literature
Javier Bonet, Richard D. Wood;
Nonlinear continuum mechanics for finite element analysis. ISBN: 0-521-57272-X
Teaching methods and learning activities
Theoretical classes with exposition of fundamental principles and small problems; practical classes with more complex problems.
Evaluation Type
Distributed evaluation with final exam
Assessment Components
| Designation |
Weight (%) |
| Exame |
50,00 |
| Teste |
50,00 |
| Total: |
100,00 |
Calculation formula of final grade
Theoretical classes with lecturing of fundamental principles and small problems; practical classes with more complex problems.