PUBLICATIONS (2009)
Professor of
Mechanics of Materials and Structures
("Scienza delle Costruzioni")
PUBLISHED INTERNATIONAL JOURNAL PAPERS
- Carol, I.,
Rizzi, E., and Willam,
K. (1994), "A unified theory of elastic degradation and damage
based on a loading surface", International Journal of Solids
and Structures, 31(20), 2835-2865.
- Guzina, B.B., Rizzi,
E., Willam, K. and Pak R.Y.S. (1995), "Failure
prediction of smeared crack formulations", Journal of
Engineering Mechanics, ASCE, 121(1), 150-161.
- Rizzi, E., Carol, I.
and Willam, K. (1995), "Localization
analysis of elastic degradation with application to scalar damage",
Journal of Engineering Mechanics, ASCE, 121(4), 541-554.
- Rizzi, E., Maier, G. and Willam, K. (1996), "On failure indicators in
multi-dissipative materials", International Journal of Solids
and Structures, 33(20-22), 3187-3214.
- Loret, B. and Rizzi,
E. (1997), "Anisotropic stiffness degradation triggers onset of
strain localization", International Journal of Plasticity,
13(5), 447-459.
- Rizzi, E. and Loret,
B. (1997), "Qualitative analysis of strain localization. Part I:
Transversely isotropic elasticity and isotropic plasticity", International
Journal of Plasticity, 13(5), 461-499.
- Loret, B. and Rizzi,
E. (1997), "Qualitative analysis of strain localization. Part II:
Transversely isotropic elasticity and plasticity", International
Journal of Plasticity, 13(5), 501-519.
- Rizzi, E. and Loret,
B. (1999), "Strain localization in fluid-saturated anisotropic
elastic-plastic porous media", International Journal of
Engineering Science, 37(2), 235-251.
- Loret, B. and Rizzi,
E. (1999), "Strain localization in fluid-saturated anisotropic
elastic-plastic porous media with double porosity", Journal of
the Mechanics and Physics of Solids, 47(3), 503-530.
- Rizzi, E., Papa, E. and Corigliano, A. (2000), "Mechanical behavior of a syntactic foam: experiments and modeling", International Journal of Solids
and Structures, 37(40), 5773-5794.
- Corigliano, A., Rizzi,
E. and Papa, E. (2000), "Experimental characterization and
numerical simulations of a syntactic foam/glass fibre composite
sandwich", Composites Science and Technology, 60(11),
2169-2180.
- Carol, I.,
Rizzi, E. and Willam,
K. (2001), "On the formulation of anisotropic elastic degradation.
Part I: Theory based on a pseudo-logarithmic damage tensor rate",
International Journal of Solids and Structures, 38(4), 491-518.
- Carol, I.,
Rizzi, E. and Willam,
K. (2001), "On the formulation of anisotropic elastic degradation.
Part II: Generalized pseudo-Rankine model for
tensile damage", International Journal of Solids and
Structures, 38(4), 519-546.
- Loret, B., Rizzi,
E. and Zerfa, Z. (2001), "Relations
between drained and undrained moduli in anisotropic elastic fluid-saturated porous
media", Journal of the Mechanics and Physics of Solids,
49(11), 2593-2619.
- Papa, E., Corigliano,
A. and Rizzi, E. (2001), "Mechanical behavior of a syntactic foam/glass fibre composite
sandwich: experimental results", Structural Engineering and
Mechanics, 12(2), 169-188.
- Rizzi, E. and Carol, I. (2001), "A formulation of anisotropic
elastic damage using compact tensor formalism", Journal of
Elasticity, 64(2-3), 85-109.
- Hähner, P., Ziegenbein,
A., Rizzi, E. and Neuhäuser,
H. (2002), "Spatio-temporal analysis of Portevin-Le Chatelier
deformation bands: theory, simulation and experiment", Physical
Review B, 65(13), Art. nr. 134109, 20 pages.
- Carol, I.,
Rizzi, E. and Willam,
K. (2002), "An 'extended' volumetric/deviatoric
formulation of anisotropic damage based on a pseudo-log rate", European
Journal of Mechanics - A/Solids, 21(5), 747-772.
- Rizzi, E. and Carol, I. (2003), "Dual orthotropic damage-effect
tensors with complementary structures", International Journal
of Engineering Science, 41(13-14), 1445-1495.
- Hähner, P. and Rizzi,
E. (2003), "On the kinematics of Portevin-Le
Chatelier bands: theoretical and numerical modelling",
Acta Materialia,
51(12), 3385-3397.
- Rizzi, E. and Hähner,
P. (2004), "On the Portevin-Le Chatelier effect: theoretical modeling
and numerical results", International Journal of Plasticity,
20(1), 121-165.
- Rizzi, E. and Carol, I. (2007), "Secant stress/strain relations
of orthotropic elastic damage with dual properties", Archives
of Mechanics, 59(2), 133-171.
DISCUSSION
- Carol, I., Rizzi,
E. and Willam, K. (2008), "Discussion on
the paper: Application of some anisotropic damage model to the prediction
of failure of some complex industrial concrete structure [Pierre Badel, Vincent Godard, Jean-Baptiste
Leblond, Int. J. Solids Struct.
44 (2007), 5848-5874]", Int. J. of Solids and Structures,
45(16), 4600-4602.
PREPRINTS
- Carol, I.,
Lorefice, R., and Rizzi,
E. (2007), "A reappraisal of localization analysis of isotropic
damage/plasticity models based on a single quadratic loading surface".
- Planas-Vilanova, F., Barja,
M.A., Carol, I. and Rizzi,
E. (2008), "On the set of similarity classes of pairs of 3x3 real
symmetric matrices".
- Cocchetti, G., Colasante,
G. and Rizzi, E. (2009), "On the
analysis of minimum thickness in circular masonry arches".
- Cocchetti, G. and Rizzi,
E. (2009), "An iterative algorithm for the solution of linear
systems in structural and inverse analyses".
INTERNATIONAL BOOK PAPER
- Loret, B. and Rizzi,
E. (1998), "On the effects of inertial coupling on the wave-speeds
of elastic-plastic fluid-saturated porous media", Material
Instabilities in Solids, Eds R. de Borst and E. van der
Giessen, John Wiley & Sons Ltd., Chichester, UK, Chapter 4, 41-53.
INTERNATIONAL PROCEEDINGS PAPERS
- Carol, I., Rizzi,
E. and Willam, K. (1994), "Towards a
general formulation of elastic degradation and damage based on a loading
surface", Computational Modelling of Concrete Structures,
Proc. of EURO-C 1994, March 22-25, 1994, Innsbruck, Austria, Eds H. Mang, N. Bicanic and R. de Borst, Pineridge Press, Swansea, U.K., 1994, 199-208.
- Rizzi, E., Carol, I. and Willam, K. (1994), "Localization analysis of
constitutive models for elastic degradation", Computational
Modelling of Concrete Structures, Proc. of EURO-C 1994, March 22-25,
1994, Innsbruck, Austria, Eds H. Mang, N. Bicanic and R. de Borst, Pineridge Press,
Swansea, U.K., 1994, 425-434.
- Rizzi, E. and Willam,
K. (1994), "Spatial
discretization of strain localization",
Computer Aided Assessment and Control, Proc. of LOCALIZED DAMAGE
94, Udine, Italy, June 21-23, 1994, Eds M.H. Aliabadi, A. Carpinteri,
S. Kaliszky and D.J. Cartwright,
Computational Mechanics Publications, Southampton, U.K., 1994,
553-560.
- Rizzi, E., Willam,
K. and Carol, I. (1995), "Strain localization for constitutive
models combining plasticity with elastic degradation", Computational
Plasticity: Fundamentals and Applications, Proc. of Complas IV, Barcelona, Spain, April 3-6, 1995, Eds D.R.J. Owen and E. Oñate,
Pineridge Press, Swansea, U.K., 1995, 623-634.
- Carol, I., Rizzi,
E. and Willam, K. (1995), "Current
issues in elastic degradation and damage", Engineering
Mechanics, Proc. of 10th ASCE Engineering Mechanics Specialty
Conference, University of Colorado at Boulder, Boulder, CO, USA, May
21-24, 1995, Ed. S. Sture, ASCE, New York,
U.S.A., 1995, 521-524.
- Rizzi, E. and Willam,
K. (1995), "Constitutive singularities of combined elastic
degradation and plasticity", Engineering Mechanics, Proc.
of 10th ASCE Engineering Mechanics Specialty Conference, University of
Colorado at Boulder, Boulder, CO, USA, May 21-24, 1995, Ed. S. Sture, ASCE, New York, U.S.A., 1995, 529-532.
- Rizzi, E. and Loret,
B. (1997), "Strain localization in transversely isotropic
elastic-plastic solids", Computational Plasticity:
Fundamentals and Applications, Proc. of Complas
V, Barcelona, Spain, March 17-20, 1997, Eds
D.R.J. Owen, E. Oñate and E. Hinton, Pineridge Press, Swansea, U.K., 1997, 647-654.
- Rizzi, E. and Loret,
B. (1997), "Elastic-plastic models for fluid-saturated porous
media and inception of strain localisation", Multiple scale
analyses and coupled physical systems, Proc. of Saint-Venant Symposium, Paris, France, August 28-29, 1997,
Presses des Ponts et Chaussées,
1997, 569-576.
- Carol, I., Rizzi,
E. and Willam, K. (1998), "On the
formulation of isotropic and anisotropic damage", Computational
Modelling of Concrete Structures, Proc. of EURO-C 1998, March 31-April
3, 1998, Badgastein, Austria, Eds R. de Borst, N. Bicanic, H. Mang, G. Meschke, Balkema, Rotterdam,
Netherlands, 1998, 183-192.
- Rizzi, E., and Loret,
B. (1998), "Constitutive modeling of
fluid-saturated porous media with degrading elastic properties", Poromechanics, Proc. of Biot
Conference on Poromechanics, September 14-16,
1998, Louvain-la-Neuve, Belgium, Eds J.-F. Thimus at al., Balkema, Rotterdam,
Netherlands,
1998, 141-146.
- Carol, I., Rizzi,
E. and Willam, K. (2000), "A
formulation of isotropic and anisotropic damage with evolution laws in
pseudo-log space", European Congress on Computational
Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona,
Spain, September 11-14, 2000, CD-ROM Proc., 19 pages.
- Corigliano, A., Papa, R. and Rizzi, E. (2000), "On
the use of a syntactic foam as core for sandwich panels and as external
coating for pressurised pipelines", European Congress on
Computational Methods in Applied Sciences and Engineering, ECCOMAS
2000, Barcelona, Spain, September 11-14, 2000, CD-ROM Proc., 12 pages.
- Comi, C. and Rizzi,
E. (2000), "On
bifurcation in local and nonlocal materials with tension and compression damage",
European Congress on Computational Methods in Applied Sciences and
Engineering, ECCOMAS 2000, Barcelona, Spain, September 11-14, 2000,
CD-ROM Proc., 20 pages.
- Carol, I. and Rizzi,
E. (2002), "Some
problems of tensor calculus in the context of solid mechanics",
GEMT BCN 2002, Grups d'Estudi
de Matemàtica i Tecnologia, Barcelona,
July 2002, Eds. Enric Fossas
i Joan Solà-Morales, Facultat de Matemàtiques i Estadística, UPC, Barcelona, Spain, December 2002, ISBN:
84-688-1493-8, p. 17-23.
- Rizzi, E. and Carol, I. (2002), "Constitutive
relations of orthotropic elastic damage with dual properties",
International Symposium Anisotropic Behaviour of Damaged Materials,
ABDM 2002, Krakow-Przegorzaly, Poland, September
9-11, 2002, CD-ROM Proc., 28 pages.
- Hähner,
P., Grützun, V., Rizzi, E..
(2004), "Theoretical
and numerical modeling of strain-rate softening
instabilities: on the velocity selection of propagating Portevin--Le Chatelier
deformation bands", Proc. of 2nd International Conference
on Multiscale Materials Modeling
(MMM-II), University of California at Los Angeles, USA, October 11-15,
2004, Ed. Nasr M. Ghoniem, Printed by Mechanical
and Aerospace Engineering Department, UCLA, 205-208.
- Carol, I., Rizzi,
E. and Willam, K. (2005), "An
'extended' anisotropic damage model based on Young/Poisson
decomposition", International Conference on Fracture
(ICF11), Torino, Italy, March 20-25, 2005,
CD-ROM Proc., 6 pages.
- Rizzi, E. and Sangalli,
S. (2007), "Biomechanical
Simulations of Corneal Refractive Surgery", Modelling of
Heterogeneous Materials with Applications in Construction and Biomedical
Engineering (MHM 2007), ECCOMAS Thematic Conference, Prague, Czech
Republic, June 25-27, 2007, Eds. M. Jirásek, Z. Bittnar and H. Mang, Book+CD-ROM Proc., ISBN: 978-80-01-03762-1, p.
326-327.
- Ferrari, R. and Rizzi,
E. (2008), "On
the theory of the ellipse of elasticity as a natural discretisation
method in the design of Paderno d'Adda Bridge (Italy)", VI
International Conference on Structural Analysis of Historic Construction
(SAHC08), D'Ayala and Fodde
(Eds.), Bath, UK, July 2-4 2008, Taylor & Francis Group, London, ISBN
978-0-415-46872-5, p. 583-591.
- Rizzi, E., Brescianini,
D. and Scotti, M. (2009), "On
the optimal tuning of tuned mass dampers in structural systems",
ECCOMAS Thematic Conference - 2nd Int. Conf. on Computational Methods
in Structural Dynamics and Earthquake Engineering (COMPDYN 2009), M. Papadrakakis, N.D. Lagaros,
M. Fragiadakis (Eds.), Rhodes, Greece,
22-24 June 2009, Book of Abstracts ISBN:978-960-254-682-6, p. 254; CD-ROM
Proceedings, CD532, 24 pages.
NATIONAL PROCEEDINGS PAPERS
- Rizzi, E. (1993), "Determinazione
analitica e numerica di direzioni di localizzazione in modelli a
danneggiamento scalare'' ("Analytical
and numerical evaluation
of localization directions for scalar damage models", in Italian), Proc. of
Settimo Convegno Italiano di Meccanica Computazionale AIMETA, June 1-3, 1993, Trieste, Italy, Università degli Studi
di Trieste, Dipartimento di Ingegneria Civile, 309-314.
- Rizzi, E. (1994), "Fracture-energy-based regularization
of a scalar damage model", Proc. of
Ottavo Convegno Italiano di Meccanica Computazionale AIMETA, June 15-17, 1994, Torino, Italy, Politecnico di
Torino, Dipartimento di Ingegneria Strutturale, 107-112.
- Rizzi, E. and Loret,
B. (1997), "On the inception of strain localization in anisotropic
solids and fluid-saturated porous media", Proc. of XIII Congresso Nazionale AIMETA,
Siena, Italy, September 29-October 3, 1997, Edizioni
ETS, Pisa, 1997, Vol. III - Meccanica dei Solidi, 161-166.
- Maier, G., Corigliano,
A., Papa, E. and Rizzi, E. (1999), "Mechanical
behavior of a syntactic foam/glass fibre
composite sandwich: experimental results and numerical simulations",
XIV Congresso Nazionale
AIMETA, Como, Italy, October 6-9, 1999,
CD-ROM Proc., 10 pages.
- Rizzi, E. and Hähner
(2001), "Theoretical
analysis and numerical modelling of Portevin-Le Chatelier deformation bands", XV
AIMETA Congress of Theoretical and Applied Mechanics, Taormina, Italy, September 26-29, 2001,
CD-ROM Proc., 10 pages.
THESES
- Rizzi, E. (1990), "Simulazione
del comportamento viscoplastico di acciai ad
alte temperature sotto carichi ciclici: modelli costitutivi e calcolo per
elementi finiti" ("Simulation of viscoplastic behaviour of steel components at high temperature under cyclic load: constitutive models and
finite element computations",
in Italian), Laurea Thesis,
Politecnico di Milano, Milano, Italy.
- Rizzi, E. (1993), "Localization analysis of
damaged materials", Master Thesis, Technical Report CU/SR-93/5, CEAE
Department, University of Colorado at Boulder, U.S.A., February 1993.
- Rizzi, E. (1995), "Sulla
localizzazione delle deformazioni in materiali e strutture" ("On
strain localization in materials
and structures", in Italian),
Doctoral Thesis,
Dipartimento di Ingegneria Strutturale, Politecnico di Milano, Milano,
Italy.
TECHNICAL REPORTS
- Carol, I., Rizzi,
E. and Willam, K. (1993), "A unified
theory of elastic degradation and damage based on a loading surface'',
Technical Report CU/SR-93/2, CEAE Dept., University of Colorado,
Boulder CO 80309-0428, U.S.A., February 1993.
- Rizzi, E., Carol, I. and Willam, K. (1993), "Localization analysis of
elastic degradation with application to scalar damage", Technical
Report CU/SR-93/11, CEAE Dept., University of Colorado, Boulder CO
80309-0428, U.S.A., December 1993.
- Guzina, B., Rizzi,
E., Willam, K. and Pak, R.Y.S. (1994), "Failure
detection of smeared crack formulations'', Technical Report
CU/SR-94/1, CEAE Dept., University of Colorado, Boulder CO 80309-0428,
U.S.A., January 1994.
- Rizzi, E. and Willam,
K. (1995), "Rank-one updates and failure indicators in
multi-dissipative materials'', Technical Report CU/SR-95/1,
CEAE Dept., University of Colorado, Boulder CO 80309-0428, U.S.A., January
1995.
- Carol, I., Rizzi,
E. and Willam, K. (1998), "On the
formulation of anisotropic degradation using a pseudo-logarithmic damage
tensor", Technical Report CU/SR-98/1, CEAE Dept.,
University of Colorado, Boulder CO 80309-0428, U.S.A., January 1998.
- Carol, I., Rizzi,
E. and Willam, K. (1999), "An 'extended'
formulation of isotropic and anisotropic damage with evolution laws in
pseudo-log space", Technical Report CU/SR-99/1, CEAE
Dept., University of Colorado, Boulder CO 80309-0428, U.S.A., January
1999.
- Rizzi, E. and Carol, I. (2001), "Tensor
formalism in the formulation of elastic degradation and damage",
Technical Report GT-022, ETSECCPB-UPC, Technical University of Catalunya, E-08034 Barcelona, Spain, December 2001.
- Carol, I., Rizzi,
E. and Willam, K. (2002), "An
'extended' volumetric/deviatoric formulation of
anisotropic damage based on a pseudo-log rate", Technical
Report GT-023, ETSECCPB-UPC, Technical University of Catalunya, E-08034 Barcelona, Spain, January 2002.
- Rizzi, E. and Carol, I. (2002), "Dual
orthotropic damage-effect tensors with complementary structures",
Technical Report GT-024, ETSECCPB-UPC, Technical University of Catalunya, E-08034 Barcelona, Spain, February 2002.
- Hähner, P. and Rizzi,
E. (2002), "On
the kinematics of Portevin-Le Chatelier deformation bands: theoretical modeling and numerical results",
Technical Report 06/2002, Department of Engineering, University of
Bergamo, I-24044 Dalmine (BG), Italy, December
2002.
- Barja, M.A., Carol, I., Planas-Vilanova, F.
and Rizzi, E. (2003), "The
representation problem of pairs of symmetric second-order tensors in the
context of Solid Mechanics", Mathematics Preprint Series 343/2003, IMUB, Institut de Matemàtica, Universitat de Barcelona, E-08007 Barcelona, Spain,
December 2003.
TEACHING TEXTS
- Rizzi, E. (2003), "Alcune nozioni fondamentali sul metodo
degli elementi finiti in meccanica dei solidi", Note
per il Corso di Aggiornamento "Dal
disegno alla modellazione agli elementi finiti di componenti strutturali", Università di Bergamo,
Facoltà di Ingegneria (Dalmine), 18 pagine.
- Rizzi, E. (2005), "Statica di Aste Autoportanti",
Università di Bergamo, Facoltà di Ingegneria (Dalmine), 21 pagine
manoscritte.
- Rizzi, E. (2006), "Tracce delle Lezioni di Scienza delle
Costruzioni", Università di Bergamo, Facoltà di
Ingegneria (Dalmine),
142 pagine manoscritte.
- Rizzi,
E. and Ghilardi, F.M. (2009), "Complementi
di Scienza delle Costruzioni - Raccolta di Esercizi", Università
di Bergamo, Facoltà di Ingegneria (Dalmine), in completion.
SUPERVISED THESES
Co-Advisor,
Facoltà di Ingegneria, Politecnico di Milano:
- LARIA Mariacristina,
"Sulla localizzazione in compressione uniassiale
del calcestruzzo", Laurea in Ingegneria Civile, Relatore M. di Prisco, Correlatori P.G. Gambarova,
E. Rizzi, Politecnico di Milano, a.a. 1996/1997.
- BARONCIONI Ivan, "Comportamento
meccanico di un materiale composito con matrice epossidica e microsfere di
vetro: modelli costitutivi, loro calibrazione su basi sperimentali e
simulazioni per elementi finiti", Laurea in Ingegneria Civile,
Relatori G. Maier, E. Rizzi, Politecnico di
Milano, a.a. 1997/1998, 21 Dicembre 1998,100/100
e Lode.
- FERRARI Paolo, "Simulazioni
del comportamento anelastico quasi-fragile di un
materiale composito a matrice polimerica: studio critico comparativo",
Laurea in Ingegneria Civile, Relatori G. Maier,
E. Rizzi, Politecnico di Milano, a.a. 1998/1999,
7 Giugno 1999, 95/100.
Advisor, Facoltà di Ingegneria (Dalmine),
Università di Bergamo:
- SANGALLI Stefania, "Modellazione
della biomeccanica corneale in chirurgia refrattiva", Laurea
(Triennale) in Ingegneria Meccanica, Relatore E. Rizzi, a.a. 2004/2005, 03 Ottobre 2005, 110/110 e Lode.
- FERRARI Rosalba, "Sulla
concezione strutturale ottocentesca del ponte in ferro di Paderno d'Adda secondo la teoria dell'ellisse
d'elasticità", Laurea (Triennale) in Ingegneria Edile, Relatore
E. Rizzi, a.a. 2005/2006, 21 Dicembre 2006,
110/110 e Lode. Premio di Laurea dell'Associazione "Carlo
Maddalena", Milano, quale miglior tesi di laurea in ingegneria, bando
per sei borse di studio per giovani laureati per le Facoltà di
Architettura ed Ingegneria, 2007.
- COLASANTE Giada, "Sui
meccanismi di collasso degli archi in muratura secondo l'analisi
limite", Laurea (Triennale) in Ingegneria Edile, Relatore E.
Rizzi, Correlatore G. Cocchetti, a.a. 2006/2007, 21 Dicembre 2007, 110/110 e Lode.
Premio di Laurea dell'Associazione "Carlo Maddalena", Milano,
quale miglior tesi di laurea in ingegneria, bando per cinque borse di
studio per giovani laureati per le Facoltà di Architettura ed Ingegneria,
2008.
- RUSCONI Fabio, "Analisi
numerica per elementi discreti dei meccanismi di collasso degli archi in
muratura", Laurea (Triennale) in Ingegneria Edile, Relatore E.
Rizzi, a.a. 2006/2007, 27 Febbraio 2008,
102/110.
- BRESCIANINI Daniele,
SCOTTI Matteo, "Analisi della risposta dinamica di sistemi
strutturali con assorbitori a massa accordata", Laurea Specialistica
in Ingegneria Edile, Relatore E. Rizzi, a.a.
2006/2007, 27 Febbraio 2008, entrambi 110/110 e Lode.
- FERRARI Rosalba,
"Analisi strutturale degli elementi portanti del ponte di Paderno d'Adda", Laurea Specialistica in
Ingegneria Edile, Relatore E. Rizzi, a.a.
2008/2009, 24 Settembre 2009, 110/110 e Lode.
- FACHERIS Giovanni Mattia, "Analisi
morfologica e modellazione per elementi finiti della pila sull'arco del
ponte di Paderno d'Adda", Laurea
(Triennale) in Ingegneria Edile, Relatore E. Rizzi, Correlatore R.
Ferrari, a.a. 2008/2009, 24 Settembre 2009,
102/110.
- CHIODI Paolo, GAMBIRASIO
Luca, "Simulazione numerica in deformazioni finite di provini
metallici soggetti a torsione", Laurea Specialistica in
Ingegneria Meccanica, Relatore E. Rizzi, a.a.
2008/2009 24 Settembre 2009, rispettivamente 106/110 e 110/110 e
Lode.
Last update September 2009.