Academic Year 2023/2024 - Teacher: RAFFAELE BARBAGALLO

Expected Learning Outcomes

This course aims at enabling the students to perform the advanced mechanical design and the integrity assessment of structures and components, according to the most modern procedures.

Extensive training about finite elements modelling (FEM) will be carried out, for enabling the students to predict the structural response within the frameworks of elastoplasticity, dynamics, structural integrity and damage tolerance.

In order to achieve such objective, notions of material mechanics and experimental characterization will be delivered with a pragmatical approach, respectively addressing the latest models of material behaviour (static/dynamic plasticity, material damage/failure), and the most recent laboratory procedures for calibrating such models.

The students will assist to laboratory experiments for static and dynamic testing (motor-driven and hydraulic testing machines, Hopkinson bar equipment, data acquisition and image analysis); they will then use the experimental data for calibrating selected material models which, then, will be implemented either in the FEM analyses by way of user subroutines or in the postprocessing phase of FEM results by way of simple spreadsheet calculations.

A 3-C.F.U. section of the course will be also oriented on the Digital Image Correlation (DIC) technique for full-field displacements and strains assessment. This will train the students in preparing the specimens and acquiring and processing images, aimed at determining the evolving local strains and characteristic distances of specimens/components subjected to experimental tests.

Course Structure

Lessons and classroom/laboratory exercitations.

Required Prerequisites

Preliminary knowledge from other courses according to the rules of the "Corso di Laurea"

Attendance of Lessons


Detailed Course Content

Contents of the course (C = Classes, L = Laboratory, E = Exercitation).

1) Elastoplastic response of materials (45 h, Prof. G. Mirone)

  • C1) Introduction to plasticity - Normality rule and consistency condition – hardening – associate plasticity and yield surface – von Mises plasticity –Path dependence of plastic straining – Pressure and Lode dependent yield surfaces – Experimental determination of the hardening curve – Necking – Experimental characterization – Engineering, True and Flow curves – MLR and MVB methods for round and rectangular section specimens - Practical notions for Finite Elements (FEM) modelling;
  • L1) Laboratory experiments for characterization and flow curve validation (tensile tests of round/flat, smooth/notched specimens);
  • E1) Finite elements implementation of tensile tests and comparison of results with experimental data for FEM validation;

2) Damage mechanics and ductile failure (25 h, Prof. G. Mirone)

  • C2) Triaxiality factor and Lode angle – Rice-Tracey introductory model - Phenomenological damage models (Bao-Wierzbicki, Xue-Wierzbicki etc.) – Problems of mesh dependence for failure propagation in finite elements;
  • E2) Finite elements design of simple components / special specimens including damage models via postprocessing and/or via user subroutines;
  • L2) Laboratory Testing of components designed in E2), verification of the design predictive accuracy;

3) Dynamics and High Strain Rate effects (20 h, Prof. G. Mirone)

  • C3) Strain rate effect and models of dynamic hardening – Plastic work dissipation and self-heating in dynamics – Experimental procedures for high strain rate testing – Elastic waves propagation in rods – Split Hopkinson Tensile Bar equipment (SHTB);
  • L3) Laboratory Experiments with Split Hopkinson Tensile Bar (SHTB) - evaluation of dynamic stress-strain curves – calibration of simple models for dynamic hardening;
  • E3) Finite Elements implementation of dynamic SHTB tests;

4) Digital Image Correlation (DIC) (30 h, Prof. R. Barbagallo)

  • C4) Theory of Digital Image Correlation (DIC) - Practical aspects of DIC: distance from subject, camera resolution, speckle size -   Introduction to the DIC software GOM;
  • L4) Speckle spraying and DIC derivation of displacements and strains in Experimental tests;
  • E4) Postprocessing of experimental DIC data, Finite Elements simulation of experiments, comparison of local strain fields.

Textbook Information

[1] Course lecture notes

Course Planning

 SubjectsText References
1Elastoplastic response of materials[1]
2Damage mechanics and ductile failure[1]
3Digital Image Correlation for experimental strains measurements[1]

Learning Assessment

Learning Assessment Procedures

Oral exam is the standard form of evaluation. Exercitations and laboratory activities will be carried out for a better understanding of the concepts delivered by the course and for acquiring familiarity with them before the oral exam.

To guarantee equal opportunities and in compliance with current laws, students can request a meeting in order to plan any compensatory and/or dispensatory measure, according to the educational goals and specific needs. In this case, it is advisable to contact the CInAP (Centre for Active and Participated Integration - Services for Disabilities and/or SLD) professor of the Department where the Degree Course is included.

Examples of frequently asked questions and / or exercises

Questions about the topics discussed at lessons and short numerical applications