Numerical simulations are used with growing popularity in diverse sectors of engineering. The most important applications are those which attempt to replace expensive experiments on real structures that involve material mechanical behavior beyond their elastic limit. Such circumstance makes strong requirement for formulating material constitutive models with appropriate numerical implementation and for defining protocols for their calibration. Both problems are rather challenging when dealing with advanced materials.
In order to describe mechanical behavior of materials through an appropriate constitute model experiments are needed, but the transition from measurable quantities to sought parameters cannot always be directly established. Additional difficulty is encountered when dealing with complex constitutive models which tend to capture most of the physical processes taking place during material deforming, resulting in constitutive models with elevated number of parameters. Calibration of such models on the basis of too simple experiments, risks to identify particular solutions only, managing to fit a single experiment, thus not to be treated as material representative properties. A systematic way of resolving these difficulty is through the application of inverse analysis, centered on the minimization of a discrepancy function designed to quantify the difference between measured quantities and their counter parts, computed as a function of sought material parameters. This approach is!
more and more frequently adopted despite common mathematical difficulties, such as ill-posedness, non-uniqueness of the solution and non-convex function minimization.
Within this lecture some recent research contributions achieved by our team to the methodology of inverse analysis apt for calibration of complex constitutive models will be given. Results are presented with reference to real life engineering problems, related to diverse industrial environments. The first group of problems considers diagnostic analysis of structures based on instrumented indentation test. Results concern the development of reduced basis model for the acceleration of non-linear elasto-plastic simulations. The second group of problems concerns compaction of ceramic powders and the development of phenomenological constitutive models together with protocols for their calibration. The last group of problems, discussed within the lecture, is related to applications of porous ceramics for diesel particulate filters and catalytic substrates. Some innovative modeling techniques regarding thermally induced cracking and crack healing, observed in these materials will b!e shown.
Numerical simulations are used with growing popularity in diverse sectors of engineering. The most important applications are those which attempt to replace expensive experiments on real structures that involve material mechanical behavior beyond their elastic limit. Such circumstance makes strong requirement for formulating material constitutive models with appropriate numerical implementation and for defining protocols for their calibration. Both problems are rather challenging when dealing with advanced materials.
In order to describe mechanical behavior of materials through an appropriate constitute model experiments are needed, but the transition from measurable quantities to sought parameters cannot always be directly established. Additional difficulty is encountered when dealing with complex constitutive models which tend to capture most of the physical processes taking place during material deforming, resulting in constitutive models with elevated number of parameters. Calibration of such models on the basis of too simple experiments, risks to identify particular solutions only, managing to fit a single experiment, thus not to be treated as material representative properties. A systematic way of resolving these difficulty is through the application of inverse analysis, centered on the minimization of a discrepancy function designed to quantify the difference between measured quantities and their counter parts, computed as a function of sought material parameters. This approach is!
more and more frequently adopted despite common mathematical difficulties, such as ill-posedness, non-uniqueness of the solution and non-convex function minimization.
Within this lecture some recent research contributions achieved by our team to the methodology of inverse analysis apt for calibration of complex constitutive models will be given. Results are presented with reference to real life engineering problems, related to diverse industrial environments. The first group of problems considers diagnostic analysis of structures based on instrumented indentation test. Results concern the development of reduced basis model for the acceleration of non-linear elasto-plastic simulations. The second group of problems concerns compaction of ceramic powders and the development of phenomenological constitutive models together with protocols for their calibration. The last group of problems, discussed within the lecture, is related to applications of porous ceramics for diesel particulate filters and catalytic substrates. Some innovative modeling techniques regarding thermally induced cracking and crack healing, observed in these materials will b!e shown.
In the framework of a private-value-first-price auction, we consider the seller as a player in a game with the buyers in which he has private information about their realized valuations. We ask whether the seller can benefit by using his private information strategically. We find that in fact, depending upon his information, set of signals, and commitment power the seller may indeed increase his revenue by strategic transmission of his information. For example, in the case of two buyers with values distributed independently and uniformly on [0,1], a seller informed of the private values of the buyers, can achieve a revenue close to 1/2 by sending verifiable messages (compared to 1/3 in the standard auction), and this is the largest revenue that can be obtained with any signalling strategy.
Biological soft tissues and soft gels are difficult to study and model mathematically. Bioengineers often see them as engineering materials and try to evaluate their mechanical properties with standard testing protocols, such as tensile testing, simple shear, torsion, etc. These processes are destructive for tissues, as a sample is taken out of the body and placed in a device. The resulting measured parameters and models are expected to be very different from their in vivo counterparts. To test soft tissues properly, non¬-destructively, and non¬-invasively, we can rely on elastic waves. We can study the influence of pre¬stress on their speed and obtain the nonlinear elastic parameter by inverse analysis. This idea forms the basis of the theory of acousto-¬elasticity, which can be dated back to early works of Brillouin, and has been used successfully in the past for "hard" elastic solids such as rocks and metals. With this talk, we will explore the extension of acousto-¬elasticity to "soft" elastic solids, which can be subjected to large deformations in service. We will look at theoretical, numerical, experimental, and even clinical results, generated in particular on gels, brain, breast, and skin.
Contact: pasquale.ciarletta@polimi.it
Michel Destrade is Chair of Applied Mathematics at NUI Galway, Adjunct Professor of Solid Mechanics at Zhejiang University, Adjunct Professor of Mechanical Engineering at University College Dublin, and a member of the International Brain Mechanics and Trauma Lab. Previously, he worked successively as a Junior Marie Curie Fellow (FP4) in Mathematical Physics at University College Dublin; as a Visiting Assistant Professor in Mathematics at Texas A&M University, USA; as a Directeur de Recherche with the French National Research Agency CNRS at the Institut d'Alembert, Universite Pierre et Marie Curie, Paris, France (currently on leave), and as a Senior Marie Curie Fellow (FP7) in Mechanical Engineering at University College Dublin.
He is Reviews Editor of the Proceedings of the Royal Society A, Contributing Editor of the International Journal of Non-Linear Mechanics, Associate Editor of SIAM Journal on Applied Mathematics, Journal of the Acoustical Society of America, and Editorial Board Member of Quarterly Journal of Mechanics and Applied Mathematics, International Journal of Applied Mechanics.
His research interests are in nonlinear elasticity, in stability of elastomers and biological soft tissues, and in linear, linearised, and non-linear waves. In those fields, he has authored more than 110 publications in refereed international journals.
Ovunque nel mondo fisico che ci circonda osserviamo fenomeni irreversibili, che accadono in una direzione temporale ma non in quella opposta. Tale asimmetria è proprio ciò che ci permette di distinguere il passato dal futuro. Tuttavia, le leggi che governano la dinamica dei costituenti microscopici della materia risultano simmetriche rispetto alla direzione del tempo, e come tali appaiono in conflitto con l'irreversibilità osservata a livello macroscopico. Si pone così il problema filosofico della freccia del tempo. In questa presentazione, inseguiremo la freccia del tempo attraverso lo sviluppo di teorie fisiche come la termodinamica e la meccanica statistica.
Michel Destrade is Chair of Applied Mathematics at NUI Galway, Adjunct Professor of Solid Mechanics at Zhejiang University, Adjunct Professor of Mechanical Engineering at University College Dublin, and a member of the International Brain Mechanics and Trauma Lab. Previously, he worked successively as a Junior Marie Curie Fellow (FP4) in Mathematical Physics at University College Dublin; as a Visiting Assistant Professor in Mathematics at Texas A&M University, USA; as a Directeur de Recherche with the French National Research Agency CNRS at the Institut d'Alembert, Universite Pierre et Marie Curie, Paris, France (currently on leave), and as a Senior Marie Curie Fellow (FP7) in Mechanical Engineering at University College Dublin.
He is Reviews Editor of the Proceedings of the Royal Society A, Contributing Editor of the International Journal of Non-Linear Mechanics, Associate Editor of SIAM Journal on Applied Mathematics, Journal of the Acoustical Society of America, and Editorial Board Member of Quarterly Journal of Mechanics and Applied Mathematics, International Journal of Applied Mechanics.
His research interests are in nonlinear elasticity, in stability of elastomers and biological soft tissues, and in linear, linearised, and non-linear waves. In those fields, he has authored more than 110 publications in refereed international journals.
The one?parameter family of Jack_? measures on partitions of n is an important discrete analog of Dyson’s ? ensembles of random matrix theory. Except for ? = ½, 1, 2, which have group theoretic interpretations, the Jack_ ? measure is difficult to analyze. In the case ? = 1, the Jack measure agrees with the Plancherel measure on the irreducible representations of the
symmetric group S_n, parametrized by the partitions of n. The normal approximation for the
character ratio evaluated at the transposition (12) under the Plancherel measure has been well
studied, notably by Fulman (2005, 2006) and Shao and Su (2006). A generalization of the
character ratio under the Jack_ ? measure has also been studied by Fulman (2004, 2006) and
Fulman and Goldstein (2011). In this talk, we present results on both uniform and non?uniform
error bounds on the normal approximation for the Jack_ ? measure for ? > 0. Our results
improve those in the literature and come very close to solving a conjecture of Fulman (2004).
Our proofs use Stein’s method and zero?bias coupling. This talk is based on joint work with Le
Van Thanh.
Michel Destrade is Chair of Applied Mathematics at NUI Galway, Adjunct Professor of Solid Mechanics at Zhejiang University, Adjunct Professor of Mechanical Engineering at University College Dublin, and a member of the International Brain Mechanics and Trauma Lab. Previously, he worked successively as a Junior Marie Curie Fellow (FP4) in Mathematical Physics at University College Dublin; as a Visiting Assistant Professor in Mathematics at Texas A&M University, USA; as a Directeur de Recherche with the French National Research Agency CNRS at the Institut d'Alembert, Universite Pierre et Marie Curie, Paris, France (currently on leave), and as a Senior Marie Curie Fellow (FP7) in Mechanical Engineering at University College Dublin.
He is Reviews Editor of the Proceedings of the Royal Society A, Contributing Editor of the International Journal of Non-Linear Mechanics, Associate Editor of SIAM Journal on Applied Mathematics, Journal of the Acoustical Society of America, and Editorial Board Member of Quarterly Journal of Mechanics and Applied Mathematics, International Journal of Applied Mechanics.
His research interests are in nonlinear elasticity, in stability of elastomers and biological soft tissues, and in linear, linearised, and non-linear waves. In those fields, he has authored more than 110 publications in refereed international journals.
Additive Manufacturing (AM), commonly known as three-dimensional printing, is widely recognized as a disruptive technology, and has the potential to fundamentally change the nature of future manufacturing. Building products layer-by-layer, AM represents a paradigm shift in manufacturing with many industrial applications. It enables production of huge varieties of customized products with considerable geometric complexity, and the same time, with extended capabilities and functional performances.
Despite tremendous enthusiasm, AM faces major research challenges for widespread adoption of this innovative technology. Specifically, addressing the unique challenges associated with quality engineering of AM processes is crucial to the eventual success of AM. This talk presents an overview of quality-related issues for AM processes and products, focusing on opportunities and challenges in quality inspection, monitoring, control.
Contact: piercesare.secchi@polimi.it
Bianca Maria Colosimo is full professor in the Department of Mechanical Engineering of Politecnico di Milano (Italy), where she is Deputy Head of the Department for research. She is Editor-in-chief of the Journal of Quality Technology (www.tandfonline.com/loi/ujqt20), member of the Advisory Board of the Quality, Statistics and Reliability Section at INFORMS, Council member of ENBIS (European Network of Business and Industrial Statistics) and members of the Manufuture platform (EU). In 2017, she has been selected among the 100 experts in STEM - 100esperte.it. Since 2017, she is member of the POLIMI2040 board, whose main mission is to design long-term strategies for a technical university in Europe. In the last two years, she has been invited speaker in the professional course on Additive Manufacturing: From 3D Printing to the Factory Floor - at the Massachusetts Institute of Technology (MIT) on the topic “In-situ monitoring of Additive Manufacturing”. In 2017, she has been invited speaker of a plenary talk on “Modeling and Monitoring Methods for Complex Data”, at the Stu Hunter Research Conference (Copenhagen, Denmark).
Her research interest is mainly in the area of Quality Engineering (i.e. statistical process modeling, monitoring, control and optimization), with special attention to advanced manufacturing processes (metal additive manufacturing in particular) in the Industry4.0 framework. In this area, her main interest focuses on novel solutions for modeling and monitoring big data streams (images, videos, point clouds).
Consider the Caputo evolution equation (EE) $\partial_t^\beta u =\Delta u$ with initial condition $\phi$ on $\{0\}\times\mathbb R^d$, $\beta\in(0,1)$. As it is well known, the solution reads $u(t,x)=\mathbf E_x[\phi(B_{E_t})]$. Here $B_t$ is a Brownian motion and the independent time-change $E_t$ is an inverse $\beta$-stable subordinator. The fractional kinetic $B_{E_t}$ is a popular model for subdiffusion \cite{Meerschaert2012}, with remarkable universality properties \cite{BC11,Hai18}.\\
We substitute the Caputo fractional derivative $\partial_t^\beta$ with the Marchaud derivative. This results in a natural extension of the Caputo EE featuring a \emph{time-nonlocal initial condition} $\phi$ on $(-\infty,0]\times\mathbb R^d$. We derive the new stochastic representation for the solution, namely $u(t,x)=\mathbf E_x[\phi(-W_t,B_{E_t})]$. This stochastic representation has a pleasing interpretation due to the non-obvious presence of $W_t$, elucidating the notion of time-nonlocal initial conditions. Here $W_t$ denotes the waiting/trapping time of the fractional kinetic $B_{E_t}$. We discuss classical-wellposedness \cite{T18}, and time permitting weak-wellposedness \cite{DYZ17,DTZ18} for the respective extensions of Caputo-type EEs (such as in \cite{chen,HKT17}).
Bibliography:
Barlow, \u Cern\'y (2011). Probability theory and related fields, 149.3-4: 639-673.
Chen, Kim, Kumagai, Wang (2017). arXiv:1708.05863.
Du, Toniazzi, Zhou (2018). Preprint. Submitted in Sept. 2018.
Du, Yang, Zhou (2017). Discrete and continuous dynamical systems series B, Vol 22, n. 2.
Hairer, Iyer, Koralov, Novikov, Pajor-Gyulai (2018). The Annals of Probability, 46(2), 897-955.
Hern\'andez-Hern\'andez, Kolokoltsov, Toniazzi (2017). Chaos, Solitons \& Fractals, 102, 184-196.
Meerschaert, Sikorskii (2012). De Gruyter Studies in Mathematics, Book 43.
Toniazzi (2018). To appear in: Journal of Mathematical Analysis and Applications. arXiv:1805.02464.
Bianca Maria Colosimo is full professor in the Department of Mechanical Engineering of Politecnico di Milano (Italy), where she is Deputy Head of the Department for research. She is Editor-in-chief of the Journal of Quality Technology (www.tandfonline.com/loi/ujqt20), member of the Advisory Board of the Quality, Statistics and Reliability Section at INFORMS, Council member of ENBIS (European Network of Business and Industrial Statistics) and members of the Manufuture platform (EU). In 2017, she has been selected among the 100 experts in STEM - 100esperte.it. Since 2017, she is member of the POLIMI2040 board, whose main mission is to design long-term strategies for a technical university in Europe. In the last two years, she has been invited speaker in the professional course on Additive Manufacturing: From 3D Printing to the Factory Floor - at the Massachusetts Institute of Technology (MIT) on the topic “In-situ monitoring of Additive Manufacturing”. In 2017, she has been invited speaker of a plenary talk on “Modeling and Monitoring Methods for Complex Data”, at the Stu Hunter Research Conference (Copenhagen, Denmark).
Her research interest is mainly in the area of Quality Engineering (i.e. statistical process modeling, monitoring, control and optimization), with special attention to advanced manufacturing processes (metal additive manufacturing in particular) in the Industry4.0 framework. In this area, her main interest focuses on novel solutions for modeling and monitoring big data streams (images, videos, point clouds).
Modeling and computational analysis play an increasingly important role in bioengineering, particularly in the design of implantable ventricular assist devices (VAD) and other blood-handling devices. Numerical simulation of blood flow and associated physiological phenomena has the potential to shorten the design cycle and give the designers important insights into causes of blood damage and suboptimal performance. A set of modeling techniques is presented which are based on stabilized space-time finite element formulation of the Navier-Stokes equations. Alternate methods that represent the rotating components in an averaged sense using a rotating frame of reference will be discussed. In order to obtain quantitative hemolysis prediction, cumulative tensor-based measures of strain experienced by individual blood cells must be developed; red blood cells under shear can be modeled as deforming droplets, and their deformation tracked throughout the flow volume. The methods are applied to a simplified rotary blood pump, which is currently a subject of an inter-laboratory round-robin study.
Contact: luca.dede@polimi.it
Prof. Marek Behr obtained his Bachelor's and Ph.D. degrees in Aerospace Engineering and Mechanics form the University of Minnesota in Minneapolis. After faculty appointments at the University of Minnesota and at Rice University in Houston, he was appointed in 2004 as a Professor of Mechanical Engineering and holder of the Chair for Computational Analysis of Technical Systems at the RWTH Aachen University. Since 2006, he is the Scientific Director of the Aachen Institute for Advanced Study in Computational Engineering Science, focusing on inverse problems in engineering and funded in the framework of the Excellence Initiative in Germany. Behr advises or has advised over 50 doctoral students, and has published over 75 refereed journal articles and a number of conference publications and book chapters. He is a member of several advisory and editorial boards of international journals, Vice-President of the German Association for Computational Mechanics, and a Fellow of the International Association for Computational Mechanics.
Modelling the highly localised plume spreading during CO2 geo-sequestration using conventional synchronous time-driven simulation (TDS) has been impeded by the stringent Courant-Fredrich-Levy (CFL) condition, which leads to an excessive number of time steps and consequently long computing times. To overcome this problem, we present an asynchronous discrete event simulation (DES) scheme based on local time stepping criteria, specifically developed for the CSMP++ CO2 geo-sequestration simulator. The proposed DES method is applied to a complex and heterogeneous heuristic CO2 storage model, where it proves that DES is able to concentrate the computational effort on the active regions where fast CO2 flow occurs. As a result, the execution time for the modelling of a 5-year injection is significantly reduced from over 91 days (estimated for TDS) to only 0.5 days. This dramatic speedup facilitates the modelling of CO2 injection and long-term plume spreading behaviours at the scales of field storage sites. The benefits of the new method scale with the level of refinement of geologic detail and include a distinct increase in the level of physical realism of the simulations because fast and slow events are equally well resolved in contrast with TDS implicit schemes which are robust, but fail to resolve the events captured by the new asynchronous scheme.
Contact: paolo.zunino@polimi.it
Prof. Marek Behr obtained his Bachelor's and Ph.D. degrees in Aerospace Engineering and Mechanics form the University of Minnesota in Minneapolis. After faculty appointments at the University of Minnesota and at Rice University in Houston, he was appointed in 2004 as a Professor of Mechanical Engineering and holder of the Chair for Computational Analysis of Technical Systems at the RWTH Aachen University. Since 2006, he is the Scientific Director of the Aachen Institute for Advanced Study in Computational Engineering Science, focusing on inverse problems in engineering and funded in the framework of the Excellence Initiative in Germany. Behr advises or has advised over 50 doctoral students, and has published over 75 refereed journal articles and a number of conference publications and book chapters. He is a member of several advisory and editorial boards of international journals, Vice-President of the German Association for Computational Mechanics, and a Fellow of the International Association for Computational Mechanics.
Seminari Matematici al
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometria e Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica