Monday, April 3 |
07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
08:45 - 09:00 |
Introduction and Welcome by BIRS Staff ↓ A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions. (TCPL 201) |
09:00 - 09:45 |
Irene Fonseca: Phase Separation in Heterogeneous Media ↓ Modern technologies and biological systems, such as temperature-responsive polymers and lipid rafts, take advantage of engineered inclusions, or natural heterogeneities of the medium, to obtain novel composite materials with specific physical properties. To model such situations by using a variational approach based on the gradient theory, the potential and the wells may have to depend on the spatial position, even in a discontinuous way, and different regimes should be considered.
In the critical case case where the scale of the small heterogeneities is of the same order of the scale governing the phase transition and the wells are fixed, the interaction between homogenization and the phase transitions process leads to an anisotropic interfacial energy. The supercritical
case for fixed wells is also addressed, now leading to an isotropic interfacial energy. In the subcritical case with moving wells, where the heterogeneities of the material are of a larger scale than that of the diffuse interface between different phases, it is observed that there is no macroscopic phase separation and that thermal fluctuations play a role in the formation of nanodomains.
This is joint work with Riccardo Cristoferi (Radboud University, The Netherlands) and Likhit Ganedi (Aachen University, Germany), USA), based on previous results also obtained with Adrian Hagerty (USA) and Cristina Popovici (USA). (TCPL 201) |
09:45 - 10:30 |
Amit Acharya: Field Dislocation Mechanics, Ideal MHD, and a dual variational formulation ↓ This talk will review the fully nonlinear system (geometric and material) of Field Dislocation Mechanics to establish an exact analogy with the equations of ideal magnetohydrodynamics (ideal MHD) under suitable physically simplifying circumstances. Weak solutions with various conservation properties have been established for ideal MHD recently by Faraco, Lindberg, and Szekelyhidi (2021) using the techniques of compensated compactness and convex integration; by the established analogy, these results would seem to transfer directly to the idealization of Field Dislocation Mechanics considered. A dual variational principle will be demonstrated for this system of PDE. (TCPL 201) |
10:30 - 10:45 |
Coffee Break (TCPL Foyer) |
10:45 - 11:45 |
Elise Bonhomme: Can quasi-static evolutions of perfect plasticity be derived from brittle damage evolutions? ↓ This talk adresses the question of the interplay between relaxation and irreversibility through
evolution processes in damage mechanics, by inquiring the following question: can the quasi-static
evolution of an elastic material undergoing a process of plastic deformation be derived as the limit
model of a sequence of quasi-static brittle damage evolutions ?
This question is motivated by the static analysis by Babadjian, Iurlano and Rindler who have shown how a brittle damage model introduced by Francfort and Marigo can lead to a model of (Hencky) perfect plasticity. Problems of damage mechanics being rather described through
evolution processes, it is natural to extend this analysis to quasi-static evolutions, where the inertia is neglected. We consider the case where the medium is subjected to time-dependent boundary
conditions, in the one-dimensional setting. The idea is to combine the scaling law introduced by Babadjian, Iurlano and Rindler with the quasi-static brittle damage evolution introduced by Francfort and Garroni, and try
to understand how the irreversibility of the damage process will be expressed in the limit evolution.
Surprisingly, the interplay between relaxation and irreversibility of the damage is not stable
through time evolutions. Indeed, depending on the choice of the prescribed Dirichlet boundary
condition, the effective quasi-static damage evolution obtained may not be of perfect plasticity
type. (TCPL 201) |
11:45 - 12:30 |
Duvan Henao: Harmonic dipoles in elasticity ↓ Whenever the stored energy density of a hyperelastic material has slow growth at infinity (below |F|^p with p less than the space dimension), it may undergo cavitation (the nucleation and sudden growth of internal voids) under large hydrostatic tension [Ball, 1982; James & Spector, 1992]. This constitutes a failure of quasiconvexity and, hence, a challenge for the existence theory in elastostatics [Ball & Murat, 1984]. The obstacle has been overcome under certain coercivity hypotheses [Müller & Spector, 1995; Sivaloganathan & Spector, 2000] which, however, fail to be satisfied by the paradigmatic example in elasticity: that of 3D neo-Hookean materials. A joint work with Marco Barchiesi, Carlos Mora-Corral, and Rémy Rodiac will be presented, where this borderline case was solved for hollow axisymmetric domains. Partial results leading to a solution when the axis of rotation is contained (where the dipoles found by [Conti & De Lellis, 2003] must be proved to be non energy-minimizing) will also be discussed. (Online) |
12:00 - 13:30 |
Lunch ↓ Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
13:00 - 14:00 |
Guided Tour of The Banff Centre ↓ Meet in the PDC front desk for a guided tour of The Banff Centre campus. (PDC Front Desk) |
14:00 - 14:20 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL Foyer) |
14:30 - 15:15 |
Andrew Lorent: Differential inclusions, entropies and the Aviles Giga functional ↓ We will outline some elementary questions and theorems about differential inclusions. Then make a "discontinuous jump" and talk about the concept of entropies from scalar conservation laws and the adaption of this concept to the Aviles Giga functional. Then we show how these topics connect and how the connection has application to both differential inclusions and to the Aviles Giga. (TCPL 201) |
15:15 - 16:00 |
Coffee Break (TCPL Foyer) |
16:00 - 16:45 |
Caterina Ida Zeppieri: Homogenisation of nonlinear randomly perforated media under minimal assumptions on the size of the perforations. ↓ In this talk we discuss the homogenisation of vectorial integral functionals with q growth in a bounded domain of Rn, n>q>1, which is perforated by a random number of small spherical holes with random radii and centres. We show that for a class of stationary short-range correlated processes for the centres and radii of the holes, in the homogenised limit we obtain a nonlinear averaged analogue of the ``strange term'' obtained by Cioranescu and Murat in 1982, in the periodic case.
In our case we only require that the random radii have finite n−q-moment, which is the minimal assumption to ensure that the expectation of the nonlinear capacity of the balls is finite. Although under this assumption there are holes which overlap with probability one, we can prove that the clustering holes do not have any impact on the homogenisation procedure and the limit functional.
This is a joint work with K. Zemas (University of Muenster) and L. Scardia (Heriot Watt University). (TCPL 201) |
17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building. (Vistas Dining Room) |