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 Risorsa bibliografica obbligatoria Risorsa bibliografica facoltativa
 Scheda Riassuntiva
 Anno Accademico 2020/2021 Scuola Scuola di Ingegneria Industriale e dell'Informazione Insegnamento 096268 - COMPUTATIONAL MODELING FOR MATERIALS ENGINEERING Docente Mariani Stefano Cfu 5.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento
Ing Ind - Inf (Mag.)(ord. 270) - MI (491) MATERIALS ENGINEERING AND NANOTECHNOLOGY - INGEGNERIA DEI MATERIALI E DELLE NANOTECNOLOGIE*AZZZZ096268 - COMPUTATIONAL MODELING FOR MATERIALS ENGINEERING

 Obiettivi dell'insegnamento
 The aim of the course is to provide to basic concepts of nonlinear mechanics to approach the simulation of materials behavior at small length scales. The main topics that will be illustrated in the lectures are: Numerical methods, with particular reference to the finite element method for nonlinear problems. Constitutive modeling of materials with examples for metals and metal alloys, polymers, ceramics and composite materials. Constitutive formulation for elastic-plastic material response, brittle and ductile damaging, cohesive laws for fracture phenomena. Numerical strategies for the simulation of the brittle and ductile fracture phenomena. Non local approached for plasticity and damage mechanics.

 Risultati di apprendimento attesi
 Lectures and exercise sessions will allow students to: Analyze and understand the role of nonlinearities in a continuum mechanics frame Understand the assumptions and requirements associated to the development of a finite element code Define the proper strategy to solve the problem, either in statics or dynamics Set the proper identification and validation activities/benchmarks needed to ascertain the correctness of the mathematical frame and of its implementation

 Argomenti trattati
 In details, the following topics will be introduced: Nonlinear continuum mechanics: analysis of motion, deformation gradient; measures of deformation (Green-Lagrange and rate of deformation tensors); relationship between Green-Lagrange and rate of deformation tensors; pull-back and push-forward operations; measures of stress (Cauchy, nominal, first and second Piola-Kirchhoff tensors); conservation laws. Updated and Total Lagrangian approaches: governing equations, strong/weak forms. Total Lagrangian approach: finite element formulation. Time integration procedures. X-FEM: the eXtended Finite Element Method Linear and nonlinear elasticity and visco-elasticity; elasto-plasticity. Thermo-elasticity and continuum thermodynamics.   During the lectures, illustrative examples on micro and nanoscale mechanics (for MEMS and NEMS, carbon nanotubes, graphene sheets) applied to specific problems will be illustrated, dealing e.g. with: Nonlocal continuum damage mechanics; coupled space-time multi-scale analysis of composite delamination. Multi-scale analysis of quasi-brittle fracture in polycrystalline materials. Coupled thermo-mechanical analyses.

 Prerequisiti
 A background in standard mathematics, in order to understand how to handle partial differential equations, is required.

 Modalità di valutazione
 The final oral examination will be about the course topics. The student will be asked to propose on his/her own one specific topic to work on; upon agreement with the examiner, the student will have to critically organize the discussion into a presentation, to be publicly delivered. The student has to critically discuss the proposed topic, highlighting the relevant hypotheses and assumptions, and their physical meaning.

 Bibliografia
 Ted Belytschko, Wing Kam Liu, Brian Moran, Khalil Elkhodary, Nonlinear Finite Elements for Continua and Structures, Editore: Wiley, Anno edizione: 2013 Ellad B. Tadmor, Ronald E. Miller and Ryan S. Elliott., Continuum Mechanics and Thermodynamics, Editore: Cambridge University Press, Anno edizione: 2012, ISBN: 9781107008267 Shaofan Li and Gang Wang, Introduction to Micromechanics and Nanomechanics, Editore: World Scientific Pub., Anno edizione: 2008, ISBN: 109812814132

 Software utilizzato
 Nessun software richiesto

 Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
(hh:mm)
Ore di studio autonome
(hh:mm)
Lezione
32:30
48:45
Esercitazione
7:30
11:15
Laboratorio Informatico
10:00
15:00
Laboratorio Sperimentale
0:00
0:00
Laboratorio Di Progetto
0:00
0:00
Totale 50:00 75:00

 Informazioni in lingua inglese a supporto dell'internazionalizzazione
 Insegnamento erogato in lingua Inglese Disponibilità di materiale didattico/slides in lingua inglese Disponibilità di libri di testo/bibliografia in lingua inglese Possibilità di sostenere l'esame in lingua inglese Disponibilità di supporto didattico in lingua inglese
 schedaincarico v. 1.6.8 / 1.6.8 Area Servizi ICT 22/09/2021