IRIS Pol. Torinohttps://iris.polito.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Mon, 06 Dec 2021 22:53:01 GMT2021-12-06T22:53:01Z10271Structured deformations and applicationshttp://hdl.handle.net/11583/2722671Titolo: Structured deformations and applications
Abstract: The scope of this contribution is to present an overview of the theory of structured deformations of continua and two applications, all of which involve using this rather new formulation of mechanics problems in contexts that are different from one another, thus showing the power and versatility of the theory.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11583/27226712017-01-01T00:00:00ZConfinement of dislocations inside a crystal with a prescribed external strainhttp://hdl.handle.net/11583/2728916Titolo: Confinement of dislocations inside a crystal with a prescribed external strain
Abstract: A system of n screw dislocations in an isotropic crystal undergoing antiplane shear is studied in the framework of linear elasticity.
Imposing a suitable boundary condition for the strain, namely requesting the non-vanishing of its boundary integral, results in a confinement
effect. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient
to have n distinct dislocations lying inside the crystal. The result is obtained by formulating the problem via the core radius approach and by
studying the asymptotics as the core size vanishes. An iterative scheme
is devised to prove the main result. This work sets the basis for studying
the upscaling problem, i.e., the limit as n → ∞, which is treated in [17].
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11583/27289162018-01-01T00:00:00ZRenormalized energy and Peach-Köhler forces for screw dislocations with antiplane shearhttp://hdl.handle.net/11583/2722531Titolo: Renormalized energy and Peach-Köhler forces for screw dislocations with antiplane shear
Abstract: We present a variational framework for studying screw dislocations subject to antiplane shear. Using a classical model developed by Cermelli and Gurtin [6], methods of Calculus of Variations are exploited to prove existence of solutions, and to derive a useful expression of the Peach-K¨ohler forces acting on a system of dislocation. This provides a setting for studying the dynamics of the dislocations, which is done in [4].
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11583/27225312017-01-01T00:00:00ZQualitative and quantitative properties of the dynamics of screw dislocationshttp://hdl.handle.net/11583/2722672Titolo: Qualitative and quantitative properties of the dynamics of screw dislocations
Abstract: This note collects some results on the behaviour of screw dislocation in an elastic medium. By using a semi-discrete model, we are able to investigate two specific aspects of the dynamics, namely (i) the interaction with free boundaries and collision events and (ii) the confinement inside the domain when a suitable Dirichlet-type boundary condition is imposed.
In the first case, we analytically prove that free boundaries attract dislocations and we provide an expression for the Peach–Koehler force on a dislocation near the boundary. Moreover, we use this to prove an upper bound on the collision time of a dislocation with the boundary, provided certain geometric conditions are satisfied. An upper bound on the collision time for two dislocations with opposite Burgers vectors hitting each other is also obtained.
In the second case, we turn to domains whose boundaries are subject to an external stress. In this situation, we prove that dislocations find it energetically favourable to stay confined inside the material instead of getting closer to the boundary. The result first proved for a single dislocation in the material is extended to a system of many dislocations, for which the analysis requires the careful treatments of the interaction terms.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11583/27226722017-01-01T00:00:00ZStructured Deformations of Continua: Theory and Applicationshttp://hdl.handle.net/11583/2722674Titolo: Structured Deformations of Continua: Theory and Applications
Abstract: The scope of this contribution is to present an overview of the theory of structured deformations of continua, together with some applications. Structured deformations aim at being a unified theory in which elastic and plastic behaviours, as well as fractures and defects can be described in a single setting. Since its introduction in the scientific community of rational mechanicists [10], the theory has been put in the framework of variational calculus [8], thus allowing for solution of problems via energy minimization. Some background, three problems and a discussion on future directions are presented.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11583/27226742018-01-01T00:00:00ZUpscaling of screw dislocations with increasing tangential strainhttp://hdl.handle.net/11583/2850832Titolo: Upscaling of screw dislocations with increasing tangential strain
Abstract: The upscaling of a system of screw dislocations in a material subject to an external strain is studied. The G-limit of a suitable rescaling of the renormalized energy is characterized in the space of probability measures. This corresponds to a discrete-to-continuum limit of the dislocations, which, as a byproduct, provides information on their distribution when the circulation of the tangential component of the external strain becomes larger and larger. Specifically, for particular choices of the limiting external strain, dislocations are shown to concentrate at the boundary of the material and to distribute as the limiting external strain.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11583/28508322020-01-01T00:00:00ZMean-field analysis of multipopulation dynamics with label switchinghttp://hdl.handle.net/11583/2850824Titolo: Mean-field analysis of multipopulation dynamics with label switching
Abstract: The mean-dield analysis of a multipopulation agent-based model is performed. The model couples a particle dynamics driven by a nonlocal velocity with a Markov-type jump process on the probability that each agent has of belonging to a given population. A general functional analytic framework for the well-posedness of the problem is established, and some concrete applications are presented, both in the cases of a discrete and continuous set of labels. In the particular case of a leader-follower dynamics, the existence and approximation results recently obtained in [G. Albi et al., Math. Models Methods Appl. Sci., 29 (2019), pp. 633{679] are recovered and generalized as a byproduct of the abstract approach proposed.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11583/28508242020-01-01T00:00:00ZUpscaling and spatial localization of non-local energies with applications to crystal plasticityhttp://hdl.handle.net/11583/2883352Titolo: Upscaling and spatial localization of non-local energies with applications to crystal plasticity
Abstract: We describe multiscale geometrical changes via structured deformations (g, G) and the non-local energetic response
at a point x via a function 9 of the weighted averages of the jumps [un](y) of microlevel deformations un at points y
within a distance r of x. The deformations un are chosen so that limn→∞ un = g and limn→∞ ∇un = G. We provide
conditions on 9 under which the upscaling “n → ∞” results in a macroscale energy that depends through 9 on (1)
the jumps [g] of g and the “disarrangement field” ∇g − G, (2) the “horizon” r, and (3) the weighting function αr
for
microlevel averaging of [un](y). We also study the upscaling “n → ∞” followed by spatial localization “r → 0” and
show that this succession of processes results in a purely local macroscale energy I(g, G) that depends through 9
upon the jumps [g] of g and the “disarrangement field” ∇g − G alone. In special settings, such macroscale energies
I(g, G) have been shown to support the phenomena of yielding and hysteresis, and our results provide a broader
setting for studying such yielding and hysteresis. As an illustration, we apply our results in the context of the plasticity
of single crystals.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11583/28833522020-01-01T00:00:00ZOptimal design of fractured media with prescribed macroscopic strainhttp://hdl.handle.net/11583/2722666Titolo: Optimal design of fractured media with prescribed macroscopic strain
Abstract: In this work we consider an optimal design problem for two-component fractured media for which a macroscopic strain is prescribed. Within the framework of structured deformations, we derive an integral representation for the relaxed energy functional. We start from an energy functional accounting for bulk and surface contributions coming from both constituents of the material; the relaxed energy densities, obtained via a blow-up method, are determined by a delicate interplay between the optimization of sharp interfaces and the diffusion of microcracks. This model has the far-reaching perspective to incorporate elements of plasticity in optimal design of composite media.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11583/27226662017-01-01T00:00:00Z(99m)Tc-human serum albumin nanocolloids: particle sizing and radioactivity distributionhttp://hdl.handle.net/11583/2722528Titolo: (99m)Tc-human serum albumin nanocolloids: particle sizing and radioactivity distribution
Abstract: Several parameters affect the biodistribution of administered nanocolloids (NC) for Sentinel Lymph Node (SLN) detection: particle size distribution, number of Tc atoms per particle and specific activity (SA). Relatively few data are available with frequently conflicting results. (99m)Tc-NC-human serum albumin (HSA) Nanocoll®, Nanoalbumon® and Nanotop® were analysed for particles' dimensional and radioactivity distribution, and a mathematical model was elaborated to estimate the number of particles involved. Commercially available kits were reconstituted at maximal SA of 11 MBq/µg HSA. Particles size distribution was evaluated by Dynamic Light Scattering. These data were related to the radioactivity distribution analysis passing labelled NC through three polycarbonate filters (15-30-50-nm pore size) under vacuum. Highest radioactivity was carried by 30-50 nm particles. The smallest ones, even though most numerous, carried only the 10% of (99m)Tc atoms. Nanocoll and Nanotop are not significantly different, while Nanoalbumon is characterized by largest particles (>30 nm) that carried the most of radioactivity (80%). Smallest particles could saturate the clearing capacity of macrophages; therefore, if the tracer is used for SLN detection, more node tiers could be visualized, reducing accuracy of SLN mapping. Manufacturers could implement technical leaflets with particle size distribution and could improve the labelling protocol to provide clinicians useful information.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11583/27225282015-01-01T00:00:00Z