Modelling and optimal design of refractories for high temperature industrial applications for a low carbon society

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Dissemination & Outreach
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Network-Wide Training


HeaTt training in Flow Control
“Hub for Employee Advanced Technical Training”

  • Module M1 - General, Online training

  • The module M1 - General explains the market served by Vesuvius, the customers it serves, the product offering and Vesuvius structure, and it provides the basic typical vocabulary for the Main Product Lines. It is available as E-learning on Key Success Factors. It is a pre-requisite to attend this training.

  • Module M2 - Iron & Steel, Vesuvius, Ghlin, March Wednesday 9 and Thursday 10, 2022

  • The objectives of this technical training are to understand the Iron & Steel production processes, understand what are the customers’ requirements, which refractory products are used in the iron and steel making processes and why, and finally learn some terminology used in the industry and in Vesuvius.

Summer School 2022



Summer School 2023




Team Building activity during the Summerschool 2023
Excursion in a mountain of Trentino


  • CS2: Careers and Communication


Local training


  1. Trento, January 17 - 28, 2022, "Advanced numerical methods for free-surface hydrodynamics" (30 hrs)
    This short course consists of a structured intensive two week programme of 30 hours of lectures on advanced numerical methods for the computation of large scale problems in free-surface hydrodynamics. The underlying mathematical models are derived from the incompressible Navier-Stokes equations. Specifically, a fully three-dimensional hydrostatic model, two-dimensional models using lateral and vertical averaging, and the one-dimensional open-channel equations are derived and discussed. Numerically, semi-implicit Eulerian-Lagrangian finite difference schemes on regular Cartesian and orthogonal unstructured grids are proposed. A new rigorous and nonlinear treatment of wetting and drying is included and computer implementation of different numerical models are suggested.

  2. Trento, January 31 - February 4, 2022, "Advanced numerical methods for hyperbolic equations " (40 hrs)
    The short course on advanced numerical methods consists of a structured intensive one-week programme of 40 hours of theoretical lectures and computer laboratory exercises on advanced numerical methods for hyperbolic partial differential equations with applications in engineering and science. The course covers finite volume methods, the exact and approximate solution of the Riemann problem, second order TVD methods, higher order ENO, WENO and discontinuous Galerkin methods, as well as the discretization of non-conservative problems. Special emphasis is put also on numerical methods that are able to handle complex geometries. In particular, unstructured finite volume and discontinuous Galerkin schemes as well as mesh-free particle methods are presented. The lectures on the theory will be supplemented with laboratory-based computer exercises to provide hands-on experience to all participants on the practical aspects of numerical methods for hyperbolic problems and applications using MATLAB programs specially designed for the course. The course is primarily designed for PhD students and post-doctoral researchers in applied mathematics, engineering, physics, computer science and other scientific disciplines. The course may also be of interest to senior researchers in industry and research laboratories, as well as to senior academics

  3. Trento, February 8-25, 2022, "Mathematical Methods for Engineering" (50 hrs)
    Partial differential equations (elliptic equations, parabolic equations, hyperbolic equations, boundary value problems). Separation of variables (solution of heat and wave equations by means of Fourier expansion, orthonormal bases, Sturm-Liouville problems, Bessel functions, Legendre and Chebyshev polynomials). Fundamental solutions and Green functions for elliptic equations (Dirac delta "function", distributions, fundamental solutions, Green functions, integral representation formula in terms of the Green function). Integral equations and the boundary element method for elliptic problems (Green formulae, interior and boundary integral representation formulae in terms of the fundamental solution, integral equation on the boundary, collocation and Galerkin formulations of the boundary element method, algebraic structure of the approximating problems). Weak formulation and the finite element method for elliptic problems (minimization problems, Euler equation of a functional, weak formulation, Lax-Milgram lemma, existence and uniqueness of the solution, Galerkin approximation, finite element methods and spectral methods, family of triangulations and basis functions, Céa lemma and error estimates, mixed formulation and Stokes problem, mixed finite element methods, Ladyzhenskaya-Babuska-Brezzi condition and error estimates, compatible choices of finite elements, algebraic structure of the discrete problems, other applications).

  4. Bolzano, 2022, "Introduction to FE Software"
    With the aim of mastering modeling in both commercial and open-source software, as well as performing thermomechanical analyses in this environment, the first task was acquiring knowledge about several computer tools. As CAE mate is a start-up company specialized in software for infrastructure monitoring, predictive maintenance and numerical simulation using artificial intelligence and simula- tion to predict the behavior of bridges, slopes, machines etc, there was plenty of opportunities for the practice.

  5. Bolzano, 2022, "Introduction to Advanced Numerical Methods"
    The main difficulty in the practical application of elastoplasticity models is related to development and implementation of incremental (i.e., finite-step) constitutive relationships. The difficulties lie in formulation and solution of the highly nonlinear constitutive update problem, consistent treatment of plastic incompressibility (or plastic volume changes), and consistent linearization of the incremental relationships. The last issue is of the utmost importance for overall computational efficiency of the finite element models because consistent linearization (consistent tangent) is needed to achieve the quadratic convergence of the Newton method.

  6. Trento, February 19-28, 2022, "Data exploration" (12 hrs)
    Data exploration and visualization, introduction to some of the bioinformatical and biostatistical tools/concepts used to explore a multidimensional dataset (PCA, Clustering, Linear Modeling, ...). The aim is to highlight the advantages and limitations of each approach. During the course the different aspects will be illustrated by live R/Python sessions on publicly available datasets. The students will be also encouraged to bring their own data to discuss and (possibly) analyse them.

  7. Belgrade, March 1 - 29, 2022, "Selected topics in Applied Mechanics" (30 hrs)
    The course covered advanced topics related to the analytical mechanics. The course provided theoretical background related to the Lagrange’s equations of second kind, the Lagrange–D'Alembert principle of virtual work and Hamiltonian principle. Practical application presented in the course dealt with oscillations of deformable bodies, problems of dynamic instabilities and some basics of multi-body dynamics.

  8. Belgrade, March 1 - 25, 2022, "Higher course in linear systems (Linear algebra and tensorial calculus)" (30 hrs)
    The "Higher Course for Linear Systems" is an advanced course in linear algebra and tensorial calculus. The course covered advanced mathematical concepts and techniques for understanding and analysing linear systems. Topics included vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization, orthogonality, least squares, and singular value decomposition. The course is designed to provide students with a deep understanding of the mathematical foundations of linear systems and to equip them with the skills and knowledge necessary to analyse and solve complex problems in fields such as control systems, signal processing, and engineering mechanics.

  9. Belgrade, March 8 - April 5, 2022, "Theory of elasticity" (30 hrs)
    The "Theory of Elasticity" course is a comprehensive study of the behaviour of solid materials under various types of loading and boundary conditions. The course covered the mathematical foundations of elasticity, including Mathematical preliminaries, Deformation: displacement and strains, Stress and equilibrium, Material behaviour – linear elastic solids, Formulation and solution strategies, Strain energy and related principles, Two-dimensional formulation, Two-dimensional problem solution, Thermoelasticity, Displacement potentials and stress functions, and Micromechanics applications. The course lasted 40 hours of lectures and aimed at delivering a strong understanding of the fundamental principles of elasticity, and the ability to apply these principles to a variety of engineering problems.

  10. Belgrade, March 8 - April 5, 2022, "Thermoelasticity" (30 hrs)
    The main goal of this course was to learn the basic principles of thermoelasticity and its applications to mechanical and structural systems. Additionally, the class covered the necessary principles of heat transfer to determine temperature distribution in different structures. Some basic practical examples were treated within the course where experimentally measured values were compared to the computed ones.

  11. Trento, March 14 – June 10, 2022: "Statistical methods and data analysis" (36 hrs)
    The aim of the course is to illustrate the basic mathematical tools for the analysis and modeling of experimental data, particularly concering the main statistical methods. The idea is not simply to describe and discuss the "cooking recipes" for the statistical treatment of data, but also to introduce and analyze in a critical way the statistical models implemented by the computation procedures, stressing their limitations and the actual interpretation of the results.

  12. Belgrade, April 3 - May 20, 2022, "Linear and nonlinear systems" (30 hrs)
    The course dealt with optimal control, least square methods and basics of theory of potimization. It covered multi input and multi output linear systems, as well as with some multi variate nonlinear systems and methods for their approximate solutions. Interpolation techniques and artificial neural networs were presented. Practical part of the course deals with programming in C++ and Python.

  13. Belgrade, April 4 - 29, 2022, "Numerical Methods" (30 hrs)
    The students gained a deep knowledge in applied numerical methods. The course provided elements of theory and the application in MATLAB. Numerical accuracy and different levels of precision were tackled. Numerical differentiation, finite differences and interpolation functions were presented in details. Tools for solving partial differential equations were covered with the applications in MATLAB. Solvers for linear equations, LU factorization, as well as Newton-Rhapson method for iterative solutions of nonlinear systems were covered.

  14. Belgrade, April 4 - 29, 2022, "Advanced Applied Mathematics" (30 hrs)
    The course dealt with partial differentual equations of first and second order, of different types, their applications in mechainics and thermodynamics. The secod part of the course was mostly dedicated to linear algebra, vector fields and tensorial calculus.

  15. Trento, May 2-4, 2022 - LIGHTEN 2nd Training School: "Computational mechanics and data-driven design of materials and structures" (24 hrs)
    Introduction to yield surface theory, Introduction to Object Oriented Programming, User material subroutines and yield surfaces implementation, Linear and nonlinear viscoelasticity implementation, Introduction to supervised learning with Gaussian Processes and Artificial Neural Networks, Introduction to Bayesian optimization, Introduction to Unsupervised Learning with k-means clustering for the SCA, Introduction to the data-driven framework.

  16. Belgrade, May 5 - 26, 2022, "Computer Modelling and Structure Calculations" (30 hrs)
    The course provided basics of different approaches used in numerical modelling of structures. Different numerical strategies were presented and critically compared. They included finite element method, finite difference method, finite volume method, and some basics of mesh-less methods, specifically those based on radial basis functions. Introduction to model reduction techniques was given up to the level of understanding available techniques with their benefits and related numerical burden for their implementation.

  17. Belgrade, May 6 - July 9, 2022, "Fracture mechanics" (30 hrs)
    The "Fracture Mechanics" course examined the behaviour of materials and structures when they are under conditions of crack initiation and propagation. The course deals with the mathematical principles of fracture mechanics, including linear elastic fracture mechanics (LEFM) and elasto-plastic fracture mechanics (EPFM), stress intensity factors, J-Integral, and stress concentration factors. The course also covered the methods for determining stress concentration coefficients and their effects on fracture behaviour. The course provided some basic knowledge required for numerical solutions of fracture mechanics problems. Basic principles related to cohesive zone crack modelling and extended finite element method were outlined.

  18. Belgrade, May 10 - June 15, 2022, "Theory of plasticity" (30 hrs)
    The "Theory of Plasticity" course is a detailed examination of the structural analysis with the material that exhausts the elastic limit. Elements of limit analysis are given with kinematic and static approaches with related theories. Combined bending and axial loading are further studied with M/N envelope as introduction to multi component stress plasticity. The most frequently used yield criteria used with phenomenological constitutive models are presented in details. Formulation of elasto-plastic constitutive models with plastic flow and deformation decomposition are given. Elements of finite deformation and solution strategies are outlined. Only basic strategies applied in computational plasticity are given.

  19. Trento, May 30 – June 1, 2022 - "Advanced aspects of geothecnical modelling" (12 hrs)
    The course provides an introduction to advanced modelling of granular materials within static and dynamic regimes, taking into account for fully and partial saturation. Some preliminaries of continuum mechanics are provided to ensure better understanding and to help to extend the main topics of this course to more advanced applications. An overview of novel constitutive models is provided with applications to practical problems of geotechnical engineering, and novel aspects revealed by advanced numerical modelling are presented and discussed.

  20. Trento, June 20-24, 2022 - "Global Optimization Methods - Theory, Techniques, and Advanced Engineering Applications" (32 hrs)
    Optimization techniques are generally classified into deterministic/local and stochastic/global methods. Although effective in terms of convergence speed, the former methods generally require a ‘domain knowledge’ since in the case of non-linear and multi-mimina functionals the initial trial solution must lie in the so-called ‘attraction basin’ of the global solution to avoid the convergence solution being trapped into local minima of the functional (i.e., wrong solutions of the problem at hand). In contrast, global optimization methods are potentially able to find the global optimum of the functional whatever the initial point/s of the search. The course will review fundamentals and main issues of optimization problems then focusing on classical/state-of-the-art and recently introduced global optimization approaches. Applicative examples including exercises covering advanced engineering applications will corroborate the theoretical concepts.

  21. Trento, August 29 - September2, 2022 - "Machine Learning and AI Methods - Theory, Techniques, and Advanced Engineering Applications" (32 hrs)
    Understanding and solving complex problems in the physical world has been an intelligent endeavor of humankind. Moreover, the study of artificial intelligence (AI) embodies the dream of designing machines like humans. Research in machine learning (ML) and, more recently, on deep learning (DL) techniques has attracted much attention in many engineering fields. With the spreading of such techniques, improvement in learning capacity may allow machines to “learn” from a large amount of physical data and “master” the physical laws in certain controlled boundary conditions. In the long run, a hybridization of fundamental physical principles with ”knowledge” from big data could unleash numerous engineering applications that used to be impossible due to the limit of data information and computational capabilities. The course aims at providing a solid background knowledge on AI and ML, with a focus on recent and competitive methodologies for the efficient and robust solution of both classification and regression problems in advanced engineering applications. Applicative examples including exercises will corroborate the theoretical concepts.

  22. Belgrade, September 4 - 28, 2022, "Nonlinear Finite Element Modelling" (30 hrs)
    The "Nonlinear Finite Element Method" course is a practical course that teaches the numerical techniques used to solve partial differential equations in engineering and physics through the Finite element method. The course covered mathematical foundations, variational formulation, weak form, the Galerkin method, and software implementation using software such as MATLAB and Python. Particularly in focus are nonlinear problems. The course introduces to the students all sources of nonlinearities that can be encountered within FE modelling and presents the main schemes and strategies for their solving. Course also provides some basic software skills by employing ABAQUS for solving nonlinear problems. Specifically, in focus were material nonlinearities.

  23. Belgrade, December 6 - 30, 2022, "Measurement of deformation and strains (Digital Image Correlation - DIC)" (30 hrs)
    The course "Measurement of Deformation and Strains" focused on the application of digital image correlation (DIC) for the measurement of deformation and strains in materials and structures. The course covered the theoretical foundations of DIC, including image acquisition, image processing, data analysis, and interpretation of results. The main part of the course was based on practical examples and laboratory exercises to provide hands-on experience in using DIC for the measurement of deformation and strains in materials and structures.

  24. Belgrade, December 15, 2022 - February 1, 2023, "Mechanics of composite materials" (30 hrs)
    The "Mechanics of Composite Materials" course delved into the behavior of composite materials under various loads and conditions. Students gained an understanding of the mathematical principles of mechanics of composite materials, including material symmetries and asymmetries, isotropic and anisotropic materials, lamination theory, and micromechanics. The course explored different types of composite materials, their properties and the methods used to model them.


  1. Belgrade, December 3 - 25, 2021, "Organization and Methods of Scientific Research and Communication"
    The students became familiar with the organization of scientific research activities. They learnt about modern means of acquiring scientifically meaningful information. It presented how the scientific papers are organized, what are the important information and how to present them. Part of the course was devoted to the preparation and presenting of scientific results on a conference.

  2. Bolzano, December, 2021, "CAEmate onboarding"
    training and onboarding process of several weeks that aimed to improve her preparation in the area of computer programming in Python language, use of modeling software and finite element software, as well as her skills in mathematics and mechanics of solids and constitutive modelling. The ESR succeeded in completing the onboarding process, obtaining good scores.

  3. Trento, January 17 - 19, 2022, "How to write a research project – basic" (10 hrs)
    Basic knowledge on how to prepare a research project for my PhD. What is the aim of the research project, what are the main steps and sections, Gannt chart and other tools.(8 hours lesson and 2 hours for a draft project preparation). Useful support for the PhD project preparation.

  4. Belgrade, Marxh 3 - May 5, 2022, "Research and publishing" (40 hrs)
    "Research and Publishing" is a course that focuses on the research process and the skills necessary for publishing scientific papers. The course covered various aspects of research, including the formulation of research questions, literature review, data collection and analysis, and the interpretation of results. It also covered the process of writing and publishing research papers, including the structure of a scientific paper, the use of appropriate research methods and statistics, and the ethical considerations of research. The course also included the different types of scientific publications, such as journal articles, conference papers, and dissertations, and the process of submitting and publishing research papers. The course is designed to provide students with the skills and knowledge necessary to conduct and publish research in their field of study, and to be able to communicate their research effectively to a broad audience.

  5. Trento, May 2 - 5, 2022, "Research to business: a technology transfer approach" (Trento, Hub Innovazione Trentino, 24 hrs)
    General Objectives: This seminar aims to provide PhD students with the fundamental concepts for helping PhD create impact from their research. In particular Students will be driven to think about the value of their research work in the market. They will explore mega-trends and markets and how to leverage the potential of innovation inside the research. They will investigate with experts the concepts of value proposition and customer, legacies and opportunities related to the IP strategies and protection. Public and private financing strategies and opportunities will be presented. Main Learning Outcomes: This seminar aims to provide PhD students with the fundamental concepts for helping PhD create impact from their research. In particular Students will be driven to think about the value of their research work in the market. They will explore mega-trends and markets and how to leverage the potential of innovation inside the research. They will investigate with experts the concepts of value proposition and customer, legacies and opportunities related to the IP strategies and protection. Public and private financing strategies and opportAt the end of the classes participants will be able to: Understanding differences when planning and developing a new entre/intra-preneurial project in different contexts, Ability to understand, create, capture value of the research project in a market, Ability to integrate the strategic role of IP and other intangible assets into the research project and future professional scenarios. Teaching and Learning Methods: Teaching and learning methods are primarily based on applied lectures, testimonials and real case studies from researchers, entrepreneurs, local and/or international business managers. They combine lectures, testimonials from professionals, discussions, individual and group work, hands-on activities and games. Participants will be evaluated with group exercise, and individual reports. Participants will be asked to reflect on their entrepreneurial skills (working in an interdisciplinary team and communicate effectively) and choose one entrepreneurial competence among the ENTRECOMP European framework to improve during the course (self-direct learning).

  6. Trento, April 21 – May 31, 2022, "Technical Scientific English" (Trento, 24 hrs)
    Courses of Technical-Scientific English (Academic Writing, Presentations and Academic Writing II) addressed to PhD Students of the scientific area. Each course has a limit of 15 students.

  7. Trento, March 17 - May 27, "Italian Beginners Course" (Trento, Language Centre CLA, 50 hrs)
    Extensive courses consist of two lessons per week of two and a quarter hours each, and last for around two and a half months (each course is 50 academic hours). OBJECTIVES Listening: Understanding basic instructions; understanding simple information such a show to reach a particular place from another one on foot or using public transport; getting the gist of the main information in simple messages and brief announcements. Reading: Understanding short, easy texts with high frequency words (simple messages on postcards, signs, directions, instructions, signs warning of danger in a public place, charts and tables, information and publicity leaflets). Speaking: Asking and answering simple questions pertaining to immediate needs on familiar topics. Communicating through simple, routine activities information regarding family, study and free time. Introducing yourself using simple expressions for greeting and saying goodbye. Expressing agreement or disagreement with other people in a simple way. Writing: Writing simple sentences, a postcard, a greetings card, an announcement to put on a noticeboard, form-filling.

  8. Trento, June 28, 2022 (online via zoom), "FAIR (Findable, Accessible, Interoperable and Reusable) Data for Horizon Europe" (UNITN Scientific Production Promotion and Evaluation Division)
    Speaker: Sandro Fiore
    Program: The seminar will focus on the relevance of the FAIR (Findable, Accesible, Interoperable and Reusable) principles for data management and data stewardship in science, on their strategic role as guidelines for data management in research and on their link with Open Science.

  9. Trento, July 7, 2022 (webinar), "Marie Skłodowska-Curie Postdoctoral Fellowships 2022 – UniTrento training session" (UNITN Research Support Division)
    Speakers: Marta Simonatto, Samanta Voltolini
    Program: Welcome and Introduction, Tips and Tricks from MSCA Fellows at UniTrento, How to Write a Competitive Marie Skłodowska-Curie Postdoctoral Fellowships proposal.

  10. Trento, October 12, 2022 (online via zoom), "How to maximise the impact of results in Horizon Europe" (UNITN Research Support Division, in collaboration with APRE (Agency for the Promotion of European Research))
    Speaker: Claudia Iasillo (APRE – Agenzia per la Promozione della Ricerca Europea, Agency for the Promotion of European Research)
    Program: Horizon Europe is the European Framework Program for Research and Innovation for the period 2021-2027. The budget of over 95 billion euros makes Horizon Europe the most ambitious research and innovation program ever. The program aims to strengthen the scientific and technological bases of the EU and the European research area, and to improve the innovative capacity, the competitiveness of the European industrial system and generate employment in Europe. Horizon Europe is an impact-driven programme aiming at funding projects with real impact on European citizens. This workshop is divided in two sessions: Session 1 (online) will provide an overview of the scientific, technological, economic and social impact of European funded projects, and it will focus on the impact criterion in the Horizon Europe proposal template (e.g. Impact Pathway, outcomes and impacts definition, how to maximise the impact, communication, dissemination and exploitation measures, etc.), including tips, tools and useful resources. This session will provide the theoretical basis for the second session. Session 2 (onsite) will be a hands-on session focusing on the impact canvas of the Horizon Europe template. Participants will work in small groups on how to write the impact section of a proposal.

  11. Trento, November 11, 2022 (webinar), "Horizon Europe from an ethical point of view" (UNITN Research Ethics and Integrity Unit Research Support Division)
    Speaker: Lisa Diependalele (policy officer, Ethics and Research Integrity Sector, DG Research and Innovation)
    Program: Ethics in Horizon Europe: general principles, The ethics issues: short overview (e.g., humans, personal data, animals, etc.), The ethics appraisal process: overview (this includes pre- and post-grant ethics review & monitoring), Serious and complex ethics issues: some examples, Tips for preparing an ethics self-assessment, Focus on Artificial Intelligence: a new ethics issue, Discussion.

  12. Trento, November 23, 2022 (webinar), "Horizon Europe from an ethical point of view" (UNITN Research Management Division, in collaboration with the Administration and Accounting Services - Povo)
    Speaker: Research Management Division and external speakers
    Program: The webinar is aimed at: teachers, male and female researchers, PhD students, research fellows, research collaborators, structure staff. The module will be dedicated to illustrating to young researchers the fundamental administrative procedures for the management of research projects (project phases, timesheet, purchase and travel procedures, ...).

External training activities


  1. Online course, January 24-28, 2022, CIMNE Winter school: "An excursion into computational methods" (40 hrs)
    CIMNE Winter School will take all its participants to an excursion into Computational Methods. It is a five days course where the travellers will have a first glance of some basic aspects on computational methods, such as linear algebra, continuum mechanics or the basics of the FEM; and will taste interdisciplinary disciplines such as High-Performance Computing, optimization and machine learning. The course will also take a look into key research topics as good programming, bibliography search and communication. CIMNE Winter School has been specially designed for PhD students taking their first steps into Computational Methods research disciplines, as well as for engineers and scientists aiming to have a first taste on Computational Methods. All of you are warmly welcomed. The course will be given by CIMNE researchers with an extensive investigation and teaching experience. It will be held virtually during the last week of January 2022: from the 24th to the 28th on streaming. All participants will receive a certificate of attendance.

  2. Online course, March 2-10, 2022 - "Hands on Continuum Mechanics with COMSOL" (35 hrs)
    The goal of this course is to understand the fundamentals of continuum mechanics through worked examples. Participants will tackle some typical problems of continuum mechanics, and will learn to implement a given problem using the weak formulation into the COMSOL software and to discuss the solution. 1) Browse a model of nonlinear solid mechanics, from the implementation to the solution. A first glance at the fundamentals of continuum mechanics: Kinematics, Constitutive, Balance laws. Differential form (strong) versus Integral form (weak). Worked example: large deformations of a hyperelastic solid under loadings. 2) Material Versus Spatial description. A continuum body as a differentiable manifold.Tell the difference between tensors: strain tensor versus stress tensor. Pull back & push forward of scalar, vector and tensor fields. Geometric elements; change of densities. 3) Solid mechanics versus Fluid mechanics. Kinematical constraints; isochoric motion. Reference stress (Piola) & Actual stress (Cauchy). Polar decomposition theorem; eigenspace of the stress tensor and of the strain tensor. 4) Non-linear solid mechanics. Worked example: large deformations of a hyperelastic solid under and distortions. Target metric. 5) Material response. Worked example: from elastic energy to the constitutive law for the stress. Transversely isotropic materials. Fiber reinforced materials. Worked example: fiber reinforced hyperelastic solid under traction. 6) Fluid dynamics. Tackling Navier Stokes equations. Worked examples: fluid in a channel; fluid around an obstacle. 7) Fluid-Structure interactions – theory. Worked examples: understand the moving mesh technique; how to write the problem of a beam immersed in a fluid. 8) Fluid-Structure interactions – practice. Worked example: implement and solve the problem of an oscillating beam immersed in a fluid.

  3. Udine, June 13-17, 2022 - 25th CISM-IUTAM International Summer School on: "Instability And Bifurcation Of Solids Including Coupled Field Phenomena" (35 hrs)
    The purpose of this course is to provide a carefully crafted state-of-the-art overview of the fundamental theories, established models and ongoing research related to instability and bifurcation phenomena in solids undergoing finite deformations, including the effects of electric fields and growth. The course will be organized around several complementary and interacting themes. A comprehensive overview of the continuum theory of materials subject to large deformation will be presented, including the constitutive equations of nonlinear elasticity, elastoplasticity, Cosserat solids, electroelasticity, residually stressed and fibre-reinforced materials, and growth in biological systems. The general theory of bifurcation, instability and non-uniqueness within the framework of the continuum theory of solids will be discussed as the setting for applications to specific examples. The equations governing linearized incremental deformation fields superimposed on a known finitely deformed configuration will be highlighted. The tensors of elastic moduli for isotropic and anisotropic materials will be derived, including their important incompressible specialization, and associated expressions for the incremental constitutive equations and boundary conditions will be provided. These are needed for the analysis of possible bifurcation of the equilibrium configuration into periodic patterns, and will be applied in order to obtain specific results for exemplary constitutive laws. Particular applications that will be described are material, surface, interface and bending instabilities of diffuse type. The notion of strong ellipticity will be introduced, and phenomena, such as the appearance of shear bands, associated with loss of ellipticity of the governing equations will be described. Localized bifurcation phenomena will be examined in detail, including localized bulging of tubes, necking of plates, shear banding, creasing and folding. Appropriate numerical formulations will be provided in order to illustrate the solutions for a range of specific boundary-value problems. A summary of the key equations of electroelasticity will also be given, leading to the corresponding incremental formulations of electroelasticity. In this context wrinkling of a thin film of dielectric elastomer, treated as a prototype actuator, can be generated by application of an electric potential between compliant electrodes on the surfaces of the film, leading to pull-in instability and dielectric breakdown, and therefore rendering the actuator ineffective. Thus, analysis of such instabilities will be included in the course since this is important for the design and integrity of such devices. The methods of stability analysis have a wide applicability in the context of the mechanics of soft tissue, particularly as related to instabilities associated with growth and remodelling. In growth and development, instabilities are used constructively by nature for the formation of structures, such as in the folding of tissues to form different parts of the brain. Aspects of stability and instability that relate to growth and the possible development of pathologies will also be discussed. The course is addressed to doctoral students and postdoctoral researchers in mechanical, civil and electrical engineering, materials science, applied physics and applied mathematics, academic and industrial researchers and practicing engineers.

  4. Aachen, June 27-30, 2022 - ECerS-FIRE Summer School: "Eco-Design of Refractories : E for Ecological, Economic, Eco-energetic" (3 days)
    The 2022 FIRE-ECerS Summer School "Eco-Design of Refractories : E for Ecological, Economic, Eco-energetic" will be held at the RWTH Aachen University, Germany from June 28th to June 29th and will be open to students and industrialists. A visit of Tata Steel plant in Ijmuiden, The Netherlands, is also planed on June 30th. This Summer School aims to promote cooperation on educational programs in refractories among the major institutions and companies of the sector. This school will favour networking between young scientists and experimented professors and experts. It will create links between different scientific communities (ceramics, refractory manufacturers, metallurgy, mechanics, thermodynamics, instrumentation, sustainable development) and between industrial and academic research. Integrating 3 aspects : fundamental approach, industrial needs, new approaches on innovations. Proposing a good balance between: the courses, an industrial tour, exchanges and conviviality.

  5. Milano, November 14-29, 2022 - "Non-linear solid mechanics" (Politecnico di Milano, 32 hrs)
    The course, open to all the interested PhD students, will be delivered online by Anna Pandolfi in the period November. Overview. Rigorous introduction to nonlinear solid mechanics, especially addressing finite kinematics, material frame indifference, constitutive models within a thermodynamic framework. Analysis of nonlinear material behaviors. Specific topics: 1. Mathematical preliminaries. Dual basis. Tensors. 2. Kinematics of deformations. Motions, kinematics of local deformation. Polar decomposition. 3. Conservation laws (mass, linear & angular momentum, energy). Thermodynamics. Virtual work principle. 4. Constitutive theories. Coleman-Noll’s theory. Material frame indifference. Thermodynamic potentials. Kinetic relations. Material classification. 5. Hyperelasticity. Elasticity symmetry. Internal constraints. Elastic materials: isotropic, transversally isotropic, anisotropic materials. 6. Finite Plasticity. Multiplicative decomposition of the deformation gradient. Exponential and logarithmic mapping. J2 plasticity. Pressure dependent plasticity. 7. Special materials: fiber reinforced tissues, liquid crystals.

  6. Milano, November 25 – December 6, 2022 - "ADVFEM – Advanced topics in the finite element method for structural analysis" (Politecnico di Milano, 28 hrs)
    Well posedness and stability in linear elasticity finite element models (prof. M.Cremonesi) Recap of finite elements basics. Introduction to the problem of locking. Incompressible elasticity and volumetric locking. Shear locking. Mixed formulations (HU-Washizu principle and alternative multi-filed forms). Reduced and selective integration techniques and equivalence with mixed methods, Spurious modes (hourglass). Nonlinear finite element modelling (prof. G. Novati) An introduction to non-linear FE analyses; iterative (Newton-Raphson) and incremental/iterative techniques. Example problems with geometrical nonlinearity (but small strains): cables and cable-nets. Example problems with material nonlinearity: nonlinear elastic bars. FE elastoplastic analysis; plasticity models in 1D and 3D (von Mises, isotropic hardening); tangent elastoplastic operators; s; finite-step problem and return mapping algorithm; incremental finite element procedure; examples. Contact modeling (prof. A. Ghisi) Contact problems in continuum mechanics. Normal contact between elastic solids (Hertzian theory). Non-Hertzian contact between elastic solids. Normal contact between inelastic solids. Tangential loading and inelastic contact. Dynamic effects and impact. Energy balance. Formulation of contact equations for finite elements. Contact interface equations. Friction models. Weak forms: Lagrangian, penalty and augmented Lagrangian formulation for implicit time integration. Penalty formulation in explicit time integration. Common difficulties in contact problems. Poorly defined surfaces, adjust initial body position, contact noise, overconstraint. Finite element modelling of large deformation problems(prof. S. Mariani) Nonlinear continuum mechanics: analysis of motion and deformation gradient; Green-Lagrange and rate of deformation tensors; pull-back and push-forward operations; measures of stress through rCauchy, 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. Implicit time integration procedures. Explicit dynamics finite element analyses (prof. U. Perego) Explicit dynamics approach to the finite element solution of nonlinear problems. Explicit vs. implicit time integration. Unconditional vs. conditional stability and time step size. CFL condition. The central difference method. Accuracy of the central difference method. Mesh size and mesh smoothing techniques. Mass lumping. Mass scaling vs. selective mass scaling in explicit dynamics.


Prof. Andrea Piccolroaz
Dipartimento di Ingegneria Civile, Ambientale e Meccanica
Università di Trento, via Mesiano, 77 I-38123 Trento (Italia)
Tel: +39 0461 282583
Fax: +39 0461 282599

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