Non-Linear Mechanics for Finite Element Analysis

Code:

PRODEM087

Acronym:

MNLMCA

Keywords
Classification	Keyword
OFICIAL	Mechanical Engineering

Instance: 2024/2025 - 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 Finite Element Method Iterative Solution of a Non-linear Equation System - Newton Raphson 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. Finite Element 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 without final exam

Assessment Components

Designation	Weight (%)
Apresentação/discussão de um trabalho científico	20,00
Trabalho escrito	80,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Apresentação/discussão de um trabalho científico	2,00
Elaboração de projeto	140,00
Estudo autónomo	20,00
Total:	162,00

Eligibility for exams

.

Calculation formula of final grade

100% for the completed assignment.