Non-Linear Mechanics for Finite Element Analysis

Code:

PRODEM087

Acronym:

MNLMCA

Keywords
Classification	Keyword
OFICIAL	Mechanical Engineering

Instance: 2021/2022 - 1S

Active?	Yes
Responsible unit:	Applied Mechanics Section
Course/CS Responsible:	Doctoral Program in Mechanical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
PRODEM	2	Syllabus since 2009/10	1	-	6	28	162

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.