Papers by giovanni zanzotto
arXiv (Cornell University), Apr 27, 2015
We develop a nonlinear, three-dimensional phase field model for crystal plasticity which accounts... more We develop a nonlinear, three-dimensional phase field model for crystal plasticity which accounts for the infinite and discrete symmetry group G of the underlying periodic lattice. This generates a complex energy landscape with countably-many G-related wells in strain space, whereon the material evolves by energy minimization under the loading through spontaneous slip processes inducing the creation and motion of dislocations without the need of auxiliary hypotheses. Multiple slips may be activated simultaneously, in domains separated by a priori unknown free boundaries. The wells visited by the strain at each position and time, are tracked by the evolution of a G-valued discrete plastic map, whose non-compatible discontinuities identify lattice dislocations. The main effects in the plasticity of crystalline materials at microscopic scales emerge in this framework, including the long-range elastic fields of possibly interacting dislocations, lattice friction, hardening, band-like vs. complex spatial distributions of dislocations. The main results concern the scale-free intermittency of the flow, with power-law exponents for the slip avalanche statistics which are significantly affected by the symmetry and the compatibility properties of the activated fundamental shears.
Acta Materialia, Aug 1, 2010
ABSTRACT Coherent stress-free (CSF) microstructures with specific morphologies are favored in sha... more ABSTRACT Coherent stress-free (CSF) microstructures with specific morphologies are favored in shape memory alloys (SMAs) when special relations are satisfied by the lattice parameters. Experimentally observed microstructures are, however, also formed at non-exact CSF conditions. Here we propose a framework for the investigation of almost compatible (i.e. non-perfectly CSF) twinned wedges in SMAs, and make a systematic study of these microstructures for two types of symmetry-breaking martensitic transformations. We determine the domains in lattice-parameter space wherein there exist, and coexist, different families of almost compatible wedges with low overall stress. We find these to be wide regions largely unrelated to the existence of special CSF relations, if any even exist, giving stress-free configurations. We propose SMA improvement can be obtained by targeting domains in lattice-parameter space wherein, besides satisfying other suitable properties, a maximum number of almost compatible microstructures can also form in the material. We develop this approach for wedges in SMAs undergoing the cubic-to-orthorhombic transformation.
John Wiley & Sons, Inc. eBooks, Oct 4, 2013
We present a new procedure for the systematic reduction of a continuum theory of martensitic tran... more We present a new procedure for the systematic reduction of a continuum theory of martensitic transformations to a spin system whose dynamics can be described by an automaton. Our prototypical model reproduces most of the experimental observations in martensites associated with criticality and power-law acoustic emission. In particular, it explains in a natural way why cyclic training is necessary to reach scale-free behavior.
Physical Review B, Aug 17, 2010
The structural parameters and phonon spectra of the five known polymorphs of zirconia are compute... more The structural parameters and phonon spectra of the five known polymorphs of zirconia are computed for pressures up to 48 GPa with density-functional perturbation theory within both the local-density and the generalized-gradient approximations. Thermoelastic properties in the quasiharmonic approximation, including Grüneisen mode parameters ͑Part I͒, and dielectric properties, including the lattice contribution and the Raman spectra ͑Part II͒ are derived from the phonon calculations and compared to results of experiments and previous computations.
Physical Review B, May 26, 2015
We study experimentally the intermittent progress of the mechanically-induced martensitic transfo... more We study experimentally the intermittent progress of the mechanically-induced martensitic transformation in a Cu-Al-Be single crystal through a full-field measurement technique: the grid method. We utilize an in-house especially designed gravity-based device, wherein a system controlled by water pumps applies a perfectly monotonic uniaxial load through very small force increments. The sample exhibits hysteretic superelastic behavior during the forward and reverse cubic-monoclinic transformation, produced by the evolution of the strain field of the phase microstructures. The in-plane linear strain components are measured on the sample surface during the loading cycle, and we characterize for the first time the strain intermittency in a number of ways, showing the emergence of power-law behavior for the strain avalanching over almost six decades of magnitude. We also describe the non-stationarity and the asymmetry observed in the forward vs. the reverse transformation. The present experimental approach, which allows for the monitoring of the reversible martensitic transformation both locally and globally in the crystal, proves useful and enhances our capabilities in the analysis and possible control of transition-related phenomena in shape-memory alloys.
Journal of Elasticity
By using modular functions on the upper complex half-plane, we study a class of strain energies f... more By using modular functions on the upper complex half-plane, we study a class of strain energies for crystalline materials whose global invariance originates from the full symmetry group of the underlying lattice. This follows Ericksen’s suggestion which aimed at extending the Landau-type theories to encompass the behavior of crystals undergoing structural phase transformation, with twinning, microstructure formation, and possibly associated plasticity effects. Here we investigate such Ericksen-Landau strain energies for the modelling of reconstructive transformations, focusing on the prototypical case of the square-hexagonal phase change in 2D crystals. We study the bifurcation and valley-floor network of these potentials, and use one in the simulation of a quasi-static shearing test. We observe typical effects associated with the micro-mechanics of phase transformation in crystals, in particular, the bursty progress of the structural phase change, characterized by intermittent stre...
arXiv (Cornell University), Nov 27, 2022
By using modular functions on the upper complex half-plane, we study a class of strain energies f... more By using modular functions on the upper complex half-plane, we study a class of strain energies for crystalline materials whose global invariance originates from the full symmetry group of the underlying lattice. This follows Ericksen's suggestion which aimed at extending the Landau-type theories to encompass the behavior of crystals undergoing structural phase transformation, with twinning, microstructure formation, and possibly associated plasticity effects. Here we investigate such Ericksen-Landau strain energies for the modelling of reconstructive transformations, focusing on the prototypical case of the square-hexagonal phase change in 2D crystals. We study the bifurcation and valley-floor network of these potentials, and use one in the simulation of a quasi-static shearing test. We observe typical effects associated with the micro-mechanics of phase transformation in crystals, in particular, the bursty progression of the structural phase change, characterized by intermittent stress-relaxation through microstructure formation, mediated, in this reconstructive case, by defect nucleation and movement in the lattice.
Physical Review B, 2015
We study experimentally the intermittent progress of the mechanically-induced martensitic transfo... more We study experimentally the intermittent progress of the mechanically-induced martensitic transformation in a Cu-Al-Be single crystal through a full-field measurement technique: the grid method. We utilize an in-house especially designed gravity-based device, wherein a system controlled by water pumps applies a perfectly monotonic uniaxial load through very small force increments. The sample exhibits hysteretic superelastic behavior during the forward and reverse cubic-monoclinic transformation, produced by the evolution of the strain field of the phase microstructures. The in-plane linear strain components are measured on the sample surface during the loading cycle, and we characterize for the first time the strain intermittency in a number of ways, showing the emergence of power-law behavior for the strain avalanching over almost six decades of magnitude. We also describe the non-stationarity and the asymmetry observed in the forward vs. the reverse transformation. The present experimental approach, which allows for the monitoring of the reversible martensitic transformation both locally and globally in the crystal, proves useful and enhances our capabilities in the analysis and possible control of transition-related phenomena in shape-memory alloys.
Behavioural Brain Research
Resting-state functional brain connectivity (rsFC) is in wide use for the investigation of a vari... more Resting-state functional brain connectivity (rsFC) is in wide use for the investigation of a variety of cognitive neuroscience phenomena. In the first phase of this study we explored the changes in EEGreconstructed rsFC in young vs. older adults, in the both the open-eyes (OE) and the closed-eyes (CE) conditions. The results showed significant differences in several rsFC network metrics in the two age groups, confirming and detailing established knowledge that aging modulates brain functional organisation. In the study's second phase we investigated the role of rsFC architecture on cognitive performance through a time-based Prospective Memory task involving participants who monitored the passage of time to perform a specific action at an appropriate time in the future. Regression models revealed that the monitoring strategy (i.e. the number of clock checks) can be predicted by rsFC graph metric, specifically, eccentricity and betweenness in the OE condition, and assortativity in the CE condition. These results show for the first time how metrics qualifying functional brain connectivity at rest can account for the differences in the way individuals strategically handle cognitive loads in the Prospective Memory domain.
Structural transformations in quasicrystals induced by higher dimensional lattice transitions
Crystal symmetry and the reversibility of martensitic transformations. Nature, 428 (6978). pp. 55... more Crystal symmetry and the reversibility of martensitic transformations. Nature, 428 (6978). pp. 55-59. ISSN 0028-0836 Link to official URL (if available):
We study the reconstructive phase transformations in crystalline solids (i.e. transformations in ... more We study the reconstructive phase transformations in crystalline solids (i.e. transformations in which the parent and product lattices have arithmetic symmetry groups admitting no finite supergroup), the best known example of which is the bcc-to-fcc transformation in iron. We first describe the maximal Ericksen-Pitteri neighborhoods in the space of lattice metrics, thereby obtaining a quantitative characterization for weak transformations. Then, focussing for simplicity on a two-dimensional setting, we construct a class of strain-energy functions which admit large strains in their domain and are invariant under the full symmetry group of the lattice; in particular, we give an explicit energy suitable for the square-to-hexagonal reconstructive transformation in planar lattices. We present a numerical scheme based on atomicscale finite elements and use it to analyze the effects of transformation cycling on a planar crystal, by means of our constitutive function. This example illustrat...
Fisica matematica.-Twinning in minerals and metals: remarks on the comparison of a thermoelastic ... more Fisica matematica.-Twinning in minerals and metals: remarks on the comparison of a thermoelastic theory with some experimental results. Generalities and mechanical twinning. Nota I di GIOVANNI ZANZOTTO(*) presentata (**) dal Corrisp. A. BRES-SAN. ABSTRACT.-In the present Note I and in a following Note II (Zanzotto 1988), we discuss, taking into account some available experimental data, the results of a thermoelastic theory of twinning in crystalline solids. Various noteworthy problems emerge, some of which involve the hypotheses that are at the very basis of the theory.
We study the mechanical response of a dislocation-free 2D crystal under homogenous shear using a ... more We study the mechanical response of a dislocation-free 2D crystal under homogenous shear using a new mesoscopic approach to crystal plasticity, a Landau-type theory, accounting for the global invariance of the energy in the space of strain tensors while operating with an infinite number of equivalent energy wells. The advantage of this approach is that it eliminates arbitrariness in dealing with topological transitions involved, for instance, in nucleation and annihilation of dislocations. We use discontinuous yielding of pristine micro-crystals as a benchmark problem for the new theory and show that the nature of the catastrophic instability, which in this setting inevitably follows the standard affine response, depends not only on lattice symmetry but also on the orientation of the crystal in the loading device. The ensuing dislocation avalanche involves cooperative dislocation nucleation, resulting in the formation of complex microstructures controlled by a nontrivial self-induce...
International Journal of Plasticity, 2020
We explore the nonlinear variational modelling of two-dimensional (2D) crystal plasticity based o... more We explore the nonlinear variational modelling of two-dimensional (2D) crystal plasticity based on strain energies which are invariant under the full symmetry group of 2D lattices. We use a natural parameterization of strain space via the upper complex Poincaré half-plane. This transparently displays the constraints imposed by lattice symmetry on the energy landscape. Quasi-static energy minimization naturally induces bursty plastic flow and shape change in the crystal due to the underlying coordinated basin-hopping local strain activity. This is mediated by the nucleation, interaction, and annihilation of lattice defects occurring with no need for auxiliary hypotheses. Numerical simulations highlight the marked effect of symmetry on all these processes. The kinematical atlas induced by symmetry on strain space elucidates how the arrangement of the energy extremals and the possible bifurcations of the strain-jump paths affect the plastification mechanisms and defect-pattern complexity in the lattice.
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Papers by giovanni zanzotto