Dettagli sull'Insegnamento per l'A.A. 2019/2020
Nome:
An introduction to continuum mechanics / An introduction to continuum mechanics
Informazioni
Crediti:
: Master Degree in Mathematical Engineering 12 CFU (b)
Erogazione:
Master Degree in Mathematical Engineering 1st anno curriculum Comune Elective
Lingua:
Inglese
![[info]](img/info16.png)
Prerequisiti
Basics on Calculus and Geometry.
Some knowledge of linear algebra and basic notions in elementary mechanics of a pointwise body could be helpful.
Obiettivi
To get familiar with kinematics of continuum, a suitable notion of force distribution, a general method delivering balance equations in continuum mechanics, the formal way of describing material properties and energy balance mainly for solid matter.
Sillabo
- Vector spaces; affine and Euclidean spaces; tensors; matrix of a tensor; symmetric and antisymmetric tensors; inverse of a tensor; tensor product; orthonormal basis; eigenvectors and eigenvalues; symmetric tensors; positive de?niteness of a tensor; antisymmetric tensors; orthogonal tensors; polar decomposition theorem; left and right stretch tensors; principal stretches; the Cayley–Hamilton theorem; Gauss and Stokes’s theorems; applications of divergence theorem.
- Placements and motions. Rigid and affine motions. Deformation gradient, stretch and rotation. Stretching and spin. Test velocity fields and force distributions. Working and stress. Working balance principle. Balance equations. Frame indifference principle. Affine bodies. Cauchy continuum. Cauchy stress and Piola-Kirchhoff stress. Material response. Material objectivity. Symmetry group and isotropy. Elastic and hyperelastic materials. Strain energy function. Constraints and reactive stress. Incompressibility. Mooney-Rivlin and neo-Hookean materials. Dissipative stress and dissipation principle. Fluids and solids. A general scheme for describing growth and relaxation via Kroner-Lee decomposition. Remodeling forces and stress. Eshelby tensor. Viscoelasticity. Numerical simulations with Comsol Multiphysics.
Descrittori di Dublino
Alla fine del corso, lo studente dovrebbe
- have knowledge of the geometrical setting of continuum mechanics as well as related topics in linear algebra and basic notions on tensor analysis.
- be able to read and understand the introductory chapters or appendices on tensor analysis in any book about continuum mechanics.
- have knowledge of the basics in non linear continuum mechanics and viscoelasticity.
- be able to formally describe basic and simple problems in mechanics of solids and soft matter and make use of state-of-the-art materials modelling.
- be able to understand both results and procedures described in a technical report or scientific paper and to take part in a discussion on the subject with colleagues.
- master the language and the use of the standard symbols and expressions which are used worldwide both in mathematics and mechanics.
- be able to browse quickly or read carefully both technical and scientific papers or to attend conferences and seminars to increase his knowledge by choosing topics he may be interested in.
Testi di riferimento
- C. Truesdell, A First Course in Rational Continuum Mechanics , Academic Press. 1977.
- M. Gurtin, An Introduction to Continuum Mechanics , Academic Press. 1981.
- P. Chadwick, Continuum Mechanics: Concise Theory and Problems , Dover Books on Physics. 1976.
Modalità d'esame
A few homework assignments and a final oral presentation and discussion about a subject related to the course topics.
Aggiornamenti alla pagina del corso
Le informazioni sulle editioni passate di questo corso sono disponibili per i seguenti anni accademici:
Per leggere le informazioni correnti sul corso, se ancora erogato, consulta il catalogo corsi di ateneo.
Ultimo aggiornamento delle informazioni sul corso: 11 maggio 2016, 12:12
English version
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