|
|
Paolo
Podio-Guidugli
Professor
Degree:
Nuclear Engineering, University of Pisa, 1964
Office: Dipartimento di Ingegneria Civile,
Università di Roma TorVergata,
Viale Politecnico, 1 -- 00133 Roma, Italy
Phone:
+39 06 7259 7051 Fax: +39 06
7259 7052
E-mail: ppg@uniroma2.it
|
RESEARCH
1. General. My
taste in research is mostly – not exclusively – for multidisciplinary
issues. As a matter of fact, in addition to engineers, I have
collaborated with many mathematicians, physicists, architects, and
medicine doctors; and I have published papers not only in journals
devoted to mechanics and the engineering sciences, but also in
mathematical, physical, architectural, and medical, journals. Generally
speaking, my research interests have always been in the field of
rational continuum
mechanics, with special attention for applications
as well as, occasionally, for foundational issues.
2. Applications.
Over the years, I
have been more and more involved in modeling and analyzing problems
originally proposed by material scientists, such as
(i) crystal growth [1];
(ii) motion of phase interfaces [2-5];
(iii) crack propagation [6,7];
(iv) film peeling [8,9].
Other lines of
research I have been busy with in the past few years are:
(v) study of thin
structures under form of rods, plates, and shells [10-16];
(vi) study and realization of tensegrity structures [18-20];
(vii)
continuum-mechanical modelling and analytical study of ferromagnetic
materials capable of large deformations [21-29], in particular, motion
of
domain walls and magnetization switching;
(viii) continuum-mechanical modelling of the
effect of deformation on the critical temperature in epitaxial films of
high-temperature superconductors [30-31].
Here
are some of the issues I have been able to give a new twist in the last
couple of years, with the help of various collaborators: as to
(v), I
have been able to put on a firm footing the question of validation by
variational convergence of the classic models of shearable rods and
plates [12,13,17]; as to (vii), I have worked out a theory of dynamic
micromagnetics incorporating thermal effects and, in particular,
accounting for the ferro/paramagnetic transition at the Curie point
[29].
Moreover, I have
been working at
(ix) clarifying
certain features of the standard model for contractile muscles, in
collaboration with Williams (Pittsburgh);
(x) modeling Active Fiber-reinforced Composites [32];
(xi) evaluating strength and stiffness of fractured vertebrae after
vertebroplasty [33];
all these are
on-going collaborations.
3. Foundational issues. I
have proposed a new mathematical definition of solidity and fluidity
[34], that I am now going to extend to nonsimple materials in
collaboration with Vianello (Milan). I have shown how the notion of
thermal displacement, a concept first introduced by Helmholtz, can be
expedient to extend the virtual working format so as to cover
thermomechanics (as well as other multiscale and multiphysics theories)
[35]. A
recent paper with my student
A. Favata and G. Tomassetti [41] extends to materials with fading
memory and materials with internal variables the additive energy
splitting and the representations for kinetic energy and inertia forces
I established in [40] for materials with instantaneous memory. And,
in collaboration with F. Schuricht (Dresden) I have continued to
scrutinize the properties of concentrated contact interactions [39], an
issue that I first brought to attention in 2004 [36-38].
4. Current. These
days, two especially hot research themes for me are:
(xii) models and
analysis of phase segregation by atomic rearrangement;
(xiii) role of Molecular Dynamics in the multiscale modeling of
transformation processes in condensed matter.
As
to (xii), I have proposed in [42] two new models of phase segregation,
without and with diffusion (that is, respectively, of the Allen-Cahn and
Cahn-Hilliard types). The segregation problems of A-C type are ruled by
a system of two evolution equations for the pair (order parameter,
chemical potential), consistent with a principle of entropy imbalance.
The first equation, a balance of the forces responsible for atomic
aggregation, is a nonlinear parabolic PDE; the second equation, a
balance of energy, is a nonlinear second-order ODE. Existence,
uniqueness and regularity of global-in-time solutions to these
segregation problems has been established in [43], but much more has to
be done to enlighten the sub ject completely; the C-H problem is
completely open.
As
to (xiii), in [44] I discuss a set of circumstances under which the
kinetic energy – and hence, the lagrangian – takes exactly the form
postulated in [PR], a paper that has set the accepted standard
for
MD simulations. I also show how one of the assumptions inducing those
circumstances – namely, irrotationality of cell motion – should be
incorporated in whatever metadynamics one runs to charter the energy
landscape of a crystalline substance, and then virtually explore it
along paths connecting local minima so as to simulate possible phase
transformations (see, e.g., [LP]). Finally, I point out a connection
between the zero-temperature Parrinello-Rahman MD and the search via
the Cauchy-Born Rule for an elastic stored energy mapping consistent
with a given intermolecular potential [EM]. Building on this knowledge,
much has to be done so as to put together an efficient approach to the
multiscale simulation of phase transformations (typically, but not
necessarily, with MD at the microscale and continuum mechanics at the
macroscale). Such an effort would require a rather unusual blend of
competences, chiefly, in addition to continuum mechanics, statistical
and computational physics and mathematical analysis.
[PR]
M. Parrinello and A. Rahman, Polymorphic transitions in single
crystals: A new molecular dynamics method. J. Appl. Phys. 52 (12)
(1981) 7182-7190.
[LP] A. Laio and M. Parrinello, Escaping free-energy minima. Proc Natl.
Acad. Sci. USA 99 (20) (2002) 12562-12566.
[EM]
W. E and P. Ming, Cauchy-Born Rule and the Stability of Crystalline
Solids: Static Problems. Arch. Rational Mech. Anal. 183 (2007) 241297.
REFERENCES
1.
On radial growth in crystallization theories of hyperbolic nature, pp.
150-167 of Motion by Mean Curvature and Related Topics, G. Buttazzo
& A. Visintin Ed.s, de Gruyter: Berlin New York 1994 (with G.
Vergara Caffarelli)
2. Cavitation and
phase transition of
hyperelastic fluids, Archive for Rational Mechanics and Analysis, Volume
92, pp. 121-136 (1986) (with G. Vergara Caffarelli and E.G. Virga).
Reprinted in Analysis and Thermomechanics, W.Noll’s Anniversary Volume,
B.D. Coleman, M. Feinberg & J. Serrin Ed.s, Springer-Verlag:
Berlin
Heidelberg, 1987
3. Equilibrium
phases and layered phase mixtures
in elasticity, Mathematical Models and Methods in Applied Sciences,
Volume 2, pp. 143-166 (1992) (with G. Vergara Caffarelli)
4. A
regularized equation for anisotropic motion-by-curvature, SIAM Journal
of Applied Mathematics, Volume 52, pp. 1111-1119 (1992) (with A. Di
Carlo and M.E. Gurtin)
5. On configurational
inertial forces at a
phase interface, Journal of Elasticity, Volume 44, pp. 255-269 (1996)
(with M.E. Gurtin)
6. Configurational
forces and the basic laws for
crack propagation, Journal of the Mechanics and Physics of Solids,
Volume 44 (6), pp. 905-927 (1996) (with M.E. Gurtin)
7.
Configurational forces and a constitutive theory for crack propagation
that allows for kinking and curving, Journal of the Mechanics and
Physics of Solids, Volume 46 (2), pp. 1-36 (1998) (with M.E. Gurtin)
8.
Peeling tapes, pp. 253-260 of Mechanics of Material Forces, P.
Steinmann and G.A. Maugin (Ed.s), vol. 11 of Advances in Mechanics and
Mathematics, Springer, 2005
9. Balancing the
force that drives the
peeling of an adhesive tape, Il Nuovo Cimento, Volume 121 B (5), pp.
531-543 (2006) (with N. Pede and G. Tomassetti)
10. Marcus
integration method for shearable plates, Journal of Elasticity, Volume
84, pp. 189-196 (2006) (with A. Tiero)
11.
How to use reactive stresses to improve plate-theory approximations of
the stress field in a linearly elastic plate-like body, International
Journal of Solids and Structures, Volume 44 (5), pp. 1337-1369 (2007)
(with M. Lembo)
12. A justification
of the Reissner-Mindlin plate
theory through variational convergence, Analysis and Applications,
Volume 5 (2), pp. 165-182 (2007) (with R. Paroni and G. Tomassetti)
13.
Deduction by scaling: a unified approach to classic plate and rod
theories. Asymptotic Analysis, Volume 51 (2), pp. 113-131 (2007) (with
B. Miara)
14. On structure
thinness, mechanical and variational,
pp. 227-242 of Variational Formulations in Mechanics: Theory and
Applications, E. Taroco, E.A. de Souza Neto, and A.A. Novotny (Ed.s),
CIMNE, 2007
15. On a
mathematical model of twisted multiwall
carbon nanotubes, Comm. SIMAI Congress, DOI: 10.1685/CSC06166, ISSN
1827-9015, Vol. 2 (2007) (with A. DiCarlo and L. Teresi)
16. Concepts in the
mechanics of thin structures. Pp. 77-110 of CISM Volume 503, A. Morassi
and R. Paroni Ed.s, Springer 2008
17.
A general linear theory of elastic plates and its variational
validation. Bollettino dell’Unione Matematica Italiana, (9) II 2009,
321-341 (with D. Percivale)
18. The tensegrity
arch at Tor Vergata: A
gateway to the university campus and a full-scale experimental
facility, Revue Francaise de G´enie Civil, Volume 7 (3), pp. 267-273
(2003)
19. The Tensegrity
Footbridge at TorVergata University in
Rome, Footbridge 2005, University Iuav of Venice (Italy) and OTUA
(France), Venezia (Italia) (with A. Micheletti, V. Nicotra and S.
Stucchi)
20. Tensegrity
modules for cable-strut systems, IASS
Symposium “Shell and Spatial Structures from Models to Realization”,
Montpellier, France, September 2004 (with A. Micheletti and V. Nicotra)
21. On the continuum
theory of deformable ferromagnetic solids,
Archive for Rational Mechanics and Analysis, Volume 136, pp. 201-233
(1996) (with A. DeSimone)
22. Inertial and
self interactions in
structured continua: liquid crystals and magnetostrictive solids,
MECCANICA, Volume 30, pp. 629-640 (1995) (with A. DeSimone)
23. On
the dynamics of deformable ferromagnets. I. Global weak solutions for
soft ferromagnets at rest, Annali di Matematica Pura e Applicata (IV),
Volume CLXXIX, pp. 331-360 (2001) (with M. Bertsch and V. Valente)
24. On dissipation
mechanisms in micromagnetics, The European Physical Journal B, Volume
19, pp. 417-424 (2001)
25. Le equazioni di
evoluzione dei continui ferromagnetici, Bollettino U.M.I. (8) 4-B, pp.
31-44 (2001)
26.
On the steady motions of a flat domain wall in a ferromagnet, The
European Physical Journal B, Volume 26 (2), pp.191-198 (2002) (with G.
Tomassetti)
27. On the evolution
of domain walls in hard
ferromagnets, SIAM Journal of Applied Mathematics, Volume 64 (6), pp.
1887-1906 (2004) (with G. Tomassetti)
28. On magnetization
switching with nonstandard dissipation, IEEE Transactions on Magnetics,
Volume 42 (11), pp. 3652-3656 (2006) (with G. Tomassetti)
29. A
thermodynamically consistent theory of the ferro/paramagnetic
transition. To appear in Archive for Rational
Mechanics and Analysis, 2009 (with T.
Roubicek and G. Tomassetti)
30.
Modeling deformation effects on Tc in epitaxial films of La_{1.9} S
r_{0.1} CuO_{4}, Physica C, Volume 371/2, pp. 117-128 (2002) (with P.
Cermelli)
31.
Effect of strain-induced electronic topological transitions on the
superconducting properties of La_{1.9} S r_{0.1}
CuO_{4}
thin films, The
European Physical Journal B, Volume 26 (1), pp. 67-74 (2002) (with
G.G.N. Angilella, G. Balestrino, P. Cermelli, and A.A. Varlamov)
32.
AFCs: active-stress vs active-strain modeling. To appear in Proc. 11th
EUROMECH- MECAMAT Conference “Mechanics of microstructured solids:
cellular materials, fibre reinforced solids and soft tissues”, Torino
(Italy), March 10-14, 2008 (with P. Nardinocchi)
33. On the
material characterization of PMMA cements for percutaneous
vertebroplasty. Submitted, 2008 (with A. D’Epifanio, S. Licoccia, S.
Masala, F. Massari, A. Micheletti, V. Nicotra, A. Ursone, and G.
Simonetti)
34.
On the aggregation state of simple materials, pp. 159-168 of
“Mathematical modeling of bodies with complicated bulk and boundary
behavior”, M. Silhavy Ed., Quaderni di Matematica, 20 (2007)
35. A virtual power
format for thermomechanics. Continuum Mechanics and Thermodynamics,
Volume 20 (8), pp. 479-487 (2009)
36.
Contact interactions, stress, and material symmetry, for nonsimple
elastic materials, Theoretical and Applied Mechanics, Volume 28-29, pp.
261-276 (2002)
37. Examples of
concentrated contact interactions in simple bodies, Journal of
Elasticity, Volume 75, pp. 167-186 (2004)
38.
On concentrated contact interactions, pp. 137-147 of Progress in
Nonlinear Differential Equations and their Applications, Volume 68,
Birkhuser (2006)
39. Concentrated
actions on cusped bodies. In preparation, 2008 (with F. Schuricht)
40.
Inertia and invariance, Annali di Matematica Pura e Applicata
(IV), Volume CLXXII, pp. 103-124 (1997)
41. Energy splitting
theorems for materials with memory. Submitted, 2009 (with A. Favata and
G. Tomassetti)
42.
Models of phase segregation and diffusion of atomic species on a
lattice, Ricerche di Matematica, Volume 55 (1), pp. 105-118 (2006)
43.
Existence and uniqueness of a global-in-time solution to a phase
segregation problem of the Allen-Cahn type. To appear in Mathematical
Models and Methods in Applied Sciences (2009) (with P. Colli, G.
Gilardi, and J. Sprekels)
44. On
Andersen-Parrinello-Rahman molecular dynamics, the related
metadynamics, and the use of the Cauchy-Born rule. In preparation, 2008
Revised: July 2009