Advanced mechanics of materials

Year
1
Academic year
2017-2018
Code
03004990
Subject Area
Cross-curricular
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Compulsory
Level
3rd Cycle Studies

Recommended Prerequisites

Mathematical analysis, Linear algebra, Continuum mechanics, Mechanics of Materials.

Teaching Methods

All the subjects are taught in the classes, their discussion being constantly promoted. Since the previous mathematical preparation of the students is insufficient, everything is presented in the blackboard – this allows the students to follow the logic behind successive statements. For the same reason, the book by Wood and Bonet is followed until the hyperelasticity – this self-contained and complete book is particularly focused on pedagogic aspects. At the beginning of each class, we present a brief revision of the most important results presented in previous classes which are required in the current one. A few application problems are solved allowing for some additional reflection over new subjects. The students are invited to interrupt the class in case any doubt arises.

Learning Outcomes

0-Civil engineers have to deal with different types of structures and processes whose mechanical behavior they have to understand, describe and analyse. The finite magnitude of deformations is often relevant, so that nonlinear theories are required. The complexity of such theories may need computational simulations, so that it is necessary to understand the subjacent numerical methods and to be able to correctly interpret the results.
1-Therefore, the student will learn to describe the motion of bodies with large deformations, to identify and establish the relevant mechanical entities, to understand and write the basic structural equations, in both weak and strong formulations, and to linearize them.
2-The students must also to dominate tensor algebra and tensor analysis, since they are the building blocks required for these theories.
3-In terms of the constitutive relations, students must know the fundaments of hyperelasticity and elastoplasticity under large deformations.

Work Placement(s)

No

Syllabus

Tensor álgebra, tensor analysis, directional derivative
Kinematics and deformations
-Body, configurations and motion. Material and spatial descriptions
-Deformation gradient tensor. Left and right Cauchy-Green tensors
-Polar decomposition of deformation gradient tensor.
-Length, volume and area change
-Green and Almansi tensors. Other strain tensors.
-Small strain tensor
Stress and equilibrium
-Euler and Cauchy stress principle
-Cauchy’s theorem about the tensions in a body.
-Strong and weak formulations of equilibrium in current and initial configurations
-Piola-Kirchhoff stress tensors
Elasticity
Plasticity and elastoplasticity
-Plastic deformation
-Yield function and rupture criteria
-Associated and non-associated flow rules
-Kinematic, isotropic and combined hardening
-Limit analyis theorems. Shakedown theorems
-Elastoplastic model with hardening / softening.

Head Lecturer(s)

Paulo Manuel Mendes Pinheiro da Providência e Costa

Assessment Methods

Continuous
Troubleshooting Report: 33.0%
Exam: 67.0%

Bibliography

Bonet and Wood, 2008, Nonlinear Continuum Mechanics for Finite Element Analysis, CUP

Ogden, 1984, Non-linear elastic deformations, Ellis Harwood

Haupt, 2002, Continuum mechanics and theory of materials, Springer

Dias da Silva, 2005, Mechanics and Strength of Materials, Springer

Arantes e Oliveira, 2007, Elementos da teoria da elasticidade, Lisbon, IST

Lubliner, 1990, Plasticity Theory, Macmillan

Atkinson and Bransby, 1978, The Mechanics of Soils – An Introduction to Critical State Soil Mechanics, McGraw-Hill