PROGETTAZIONE MECCANICA AVANZATA CON METODI SPERIMENTALI E NUMERICI

The course is divided in two sections: 9 ECTS taught by Prof. G. Mirone and 3 ECTS taught by Prof. R. Barbagallo.

Knowledge and Understanding

The course provides advanced training in Finite Element Modeling (FEM), enabling students to predict the structural response of components and structures under conditions involving elastoplasticity, dynamics, structural integrity, and damage tolerance.

To achieve this objective, students will acquire a solid background in mechanics of materials and experimental material characterization through a pragmatic approach. The course covers state-of-the-art constitutive models for material behavior (including static and dynamic plasticity, material damage, and failure) together with the latest laboratory procedures for the calibration of these models.

Applying Knowledge and Understanding

The course aims to provide students with the skills required to perform advanced mechanical design and structural integrity assessment of components and structures using modern engineering procedures.

Students will attend laboratory experiments involving both static and dynamic testing (servo-electric and servo-hydraulic testing machines, Split Hopkinson Bar equipment, data acquisition systems, and digital image analysis). The resulting experimental data will be used to calibrate the selected constitutive material models, which will subsequently be implemented in FEM analyses through user-defined subroutines and in the post-processing stage by means of simple spreadsheet-based calculations.

The 3 ECTS module is dedicated to Digital Image Correlation (DIC) for full-field displacement and strain measurements, as well as thermal methods for fatigue assessment. Students will be trained in specimen preparation, image acquisition, and image processing techniques aimed at determining local strain fields and characteristic lengths in specimens and structural components subjected to experimental testing, as well as evaluating their fatigue limit through thermographic measurements.

The acquired competencies are applicable to quality management in civil, industrial, and service-sector organizations, in accordance with United Nations Sustainable Development Goals (SDGs) 9 and 11 of the 2030 Agenda.

Teaching Methods

The course includes lectures, experimental data analysis sessions, classroom exercises, and laboratory activities.

Should the course be delivered in a blended or fully online format, any necessary modifications to the teaching methods may be introduced while ensuring full compliance with the syllabus and intended learning outcomes.

Prerequisites

Students are required to have attended and/or successfully completed the prerequisite courses established by the degree programme regulations.

Attendance

Attendance is mandatory.

Contents of the 9 ECTS Module (Prof. G. Mirone)

1. Elastoplastic Response of Materials

Lectures (C1)

• Introduction to plasticity.
• Normality rule and consistency condition.
• Hardening mechanisms.
• Associated plasticity and yield surfaces.
• von Mises plasticity.
• Path dependence of plastic deformation.
• Pressure- and Lode-dependent yield criteria.
• Experimental determination of hardening curves.
• Necking.
• Experimental characterization of materials.
• Engineering, true, and flow stress-strain curves.
• MLR and MVB methods for round and rectangular specimens.
• Practical aspects of Finite Element Modeling (FEM).

Laboratory (L1)

• Experimental characterization and validation of flow curves through tensile testing of smooth and notched specimens with round and flat cross-sections.

Exercises (E1)

• Finite element simulation of tensile tests and comparison between numerical and experimental results for FEM validation.

2. Damage Mechanics and Ductile Failure

Lectures (C2)

• Stress triaxiality and Lode angle.
• Introduction to the Rice–Tracey model.
• Phenomenological damage models (Bao–Wierzbicki, Xue–Wierzbicki, etc.).
• Mesh dependency issues in finite element simulations of failure propagation.

Exercises (E2)

• Finite element design of simple components and specially designed specimens, including damage modeling through post-processing techniques and/or user-defined subroutines.

Laboratory (L2)

• Experimental testing of the components and specimens designed during Exercise E2, with verification of the predictive accuracy of the numerical models.

3. Dynamics and High-Strain-Rate Effects

Lectures (C3)

• Strain-rate effects and dynamic hardening models.
• Plastic work dissipation and adiabatic self-heating.
• Experimental procedures for high-strain-rate testing.
• Elastic wave propagation in rods.
• Split Hopkinson Tensile Bar (SHTB) testing system.

Laboratory (L3)

• Split Hopkinson Tensile Bar experiments.
• Determination of dynamic stress-strain curves.
• Calibration of constitutive models for dynamic hardening.

Exercises (E3)

• Finite element implementation and simulation of dynamic SHTB tests.

Reference Material

Course lecture notes.

Learning Assessment

Assessment consists of an oral examination covering both theoretical topics and simple numerical applications of constitutive models and analytical formulations.

If required by exceptional circumstances, assessment may also be conducted remotely.

To ensure equal opportunities and full compliance with current regulations, students with specific learning needs may request an individual meeting to discuss appropriate compensatory and/or dispensatory measures, consistent with the course learning objectives and their specific requirements. Students may also contact the departmental representative of the CInAP (Centre for Active and Participatory Inclusion – Services for Students with Disabilities and/or Specific Learning Disorders).

Lessons and classroom / laboratory exercitations, postprocessing of data from experimental  tests

Contents of the course (C = classes, L = lab., 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) modeling;
• 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 inculding damage models via postprocessing and/or via user subroutines;
• L2) Lab. Testing of components designed in E2), verificarion 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) Lab. 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;

[1] Course lecture notes and selected publications are used as reference