Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2019/2020
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Docente Foletti Stefano
Cfu 10.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

The modern engineering is more than ever characterised by the use of all classes of materials and by the possibility of design new materials by adopting new technologies. A clear understanding of the mechanical behaviour of materials is necessary to optimize the material selection, to study the interaction between material and shape and to critically apply design rules in order to avoid unexpected failure of components. The goal of the course Modelling of Mechanical Behaviour of Materials A (MMBM-A 10 CFU) and B (MMBM-B 6 CFU) is to provide the students with the specifics of the mechanical behaviour of different material classes. Each material will be studied considering its own peculiarities in terms of specific constitutive laws, strength and specific life assessment methods under complex stress states. Some material properties will be experimentally evaluated in three experimental laboratories following international standards for material characterization. The students attending the course MMBM-A will apply all the course contents in several numerical laboratories where the mechanical behaviour of materials will be numerically modelled by adopting the finite element method approach.

Risultati di apprendimento attesi

The course provides an adequate preparation on the mechanical behaviour of polymers, composite materials, metals and advanced materials for the design of mechanical components with a great attention to the life cycle assessment methods of components and products under a complex stress state.


Knowledge and understanding. On successful completion of this course, students will be able to:

  • Explain the concepts of elasticity, plasticity, fatigue and fracture of different materials;
  • Explain various failure theories for different materials;
  • Explain the concepts of stress-based fatigue, strain-based fatigue, and fatigue crack-growth under a complex stress state;
  • Explain the concept of fracture toughness and its use in engineering design;
  • Compare the mechanical, fatigue and fracture properties of materials.


Applying knowledge and understanding. During the course, students will:

  • Analyse composite laminates for stresses and strains and predict failure;
  • Analyse structures for stresses and strains and predict fatigue failure under high cycle and low cycle fatigue conditions;
  • Use the concept of elasto-plastic fracture mechanics and estimate the effect of cracks in materials and structures by defining the failure assessment diagram;
  • Apply the standard test methods for tensile testing, strain-controlled fatigue testing and measurements of fracture toughness in the experimental laboratories.


Making judgement and learning skills (Only for students of MMBM-A).  In Numerical Lab, under the supervision of a tutor, the students will learn how to:

  • Calibrate material models starting from experimental data;
  • Simulate the mechanical behaviour of different materials in finite element analyses;
  • Create finite element models of real mechanical components and apply the different failure theories for a safe design.

Argomenti trattati

Topic 1 - Optimization of materials selection: overview of available materials for the production of components and machinery parts, method of optimal materials selection (Ashby charts).

Topic 2 - Polymers: classification, visco-elastic behaviour and models, strength/crazing, hyperelastic behaviour and models.

Topic 3 - Composite materials: definition and classification, reminder of elasticity of anisotropic and orthotropic materials, mechanical characterization, rule of mixture, static strength and failure criteria, laminated structures, lamination theory.

Topic 4 - Metals: life assessment methods of components and products under a complex stress states, multiaxial high cycle fatigue (critical plane and stress invariants approaches), uniaxial low cycle fatigue (cyclic behaviour and strain based approach to fatigue), elasto-plastic behaviour under multiaxial cyclic loading (Chaboche cyclic plasticity model), multiaxial low cycle fatigue (strain based criteria, energetic approach, critical plane approach), plasticity effect in fracture (J integral, Dugdale model, failure assessment diagram).

Topic 5 - Advanced materials for the design of mechanical components: mechanical characterization, static and fatigue properties of ceramic materials, smart materials and shape memory alloys.

Topic 6 – Development of analytical tools: design of a composite laminate under a general loading condition, high cycle fatigue and low cycle fatigue assessment, failure assessment diagram.

Topic 7 - Experimental laboratories: mechanical characterization of unidirectional composites, low cycle fatigue behaviour, fracture toughness.

Topic 8 – Numerical laboratories on modelling and simulation of mechanical behaviour of materials: structural optimization; modelling of the hyperelastic and viscoelastic material behaviour; specific methods of numerical modelling for long fibre composites, laminates and sandwich panels; numerical modelling of metals: elastic and elasto-plastic behaviour in finite element analysis, finite element in fracture mechanics.


Depending on the class (MMBM-A or -B, marked out by different credits) different programs are foreseen:

MBMB A (10CFU - 9 hours/week): topics 1-8. The numerical laboratory (Topic 8) is integral part of the course. The objective of the lab is to help students in applying the theories and principles learned during the class. The numerical laboratory will be supervised by a tutor. The evaluation of numerical labs will be based on a report and a presentation during the final examination. Students who cannot take the numerical laboratory in this semester can work at the project on their own. In this case, no support by tutor will be possible.

MBMB B (6CFU - 5 hours/week): topics 1-7


Students are required to know the principles of elasticity of isotropic materials, strength of metals and assessment criteria (3D state of stress, multiaxial failure theories), uniaxial high cycle fatigue, linear elastic fracture mechanics, finite element modelling (only for students of MMBM-A).


Detailed description:

Strength of materials and assessment criteria: elastic deformation of isotropic materials, principal stresses and maximum shear stress, three-dimensional states of stress, stresses on the octahedral planes, complex state of strain, 3D state of stress, multiaxial failure theories.

Fatigue of Materials: High Cycle Fatigue. Endurance limit, Fatigue strength, Modifying factors, Stress Concentration and Notch Sensitivity, Variable Amplitude loading, Cumulative Fatigue damage.

Linear Elastic Fracture Mechanics: energy approach (Griffith), Stress Intensity Factor, KIC, Crack Propagation

Fatigue Crack Growth: Paris equation, effects of stress ratio on fatigue crack growth, trends in fatigue crack growth behavior, life estimates for constant amplitude loading.

Computer skills: basic knowledge of numerical computing software (Recommended: Matlab)


Only for students of MMBM-A: 

Finite element modelling: basic formulation, definition of stiffness matrix, main shape functions.

Computer skills: basic knowledge of finite element software (Recommended: Abaqus)

Modalità di valutazione

Students’ knowledge, understanding and communication abilities will be evaluated by an oral exam covering the full program of the course both on theoretical aspects and their application to mechanical components (application of knowledge and understanding).


Numerical Lab report (Only for students of MMBM-A). Only for MMBM-A course, to check if the students got the Making Judgements, Learning skills and Communication abilities, the students are required to present a report on numerical laboratories. Students will be asked to present one or more numerical labs during the oral exam. The Lab Report is mandatory and its assessment will follow a Pass - not Pass scheme without a grade.

Experimental Lab report. The students are required to present a report on experimental laboratories. Students will be asked to present and discuss one experimental labs during the oral exam. The Exp Report is mandatory and its assessment will follow a Pass - not Pass scheme without a grade.

Risorsa bibliografica facoltativaP.K. Mallick, Fiber-Reinforced Composites (Materials, Manufafacturing and Design), Editore: CRC Press

e-book PoliMi

Risorsa bibliografica facoltativaD. Socie, G. Marquis, Multiaxial Fatigue, Editore: SAE International, ISBN: 978-0-7680-0453-3

Software utilizzato
Nessun software richiesto

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 100:00 150:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
schedaincarico v. 1.8.3 / 1.8.3
Area Servizi ICT