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Résumé séminaire K. Dayal

"Nonlocal Models of Microstructure in Active Materials"

Active or multifunctional materials are important for a range of applications such as actuation, sensing, energy-harvesting. The unusual properties of these materials is often driven by changes in microstructure due to applied fields.
As nanoscale fabrication grows increasingly sophisticated, it allows fabrication of devices near the microstructural lengthscales.
This provides a range of challenges to mechanics involving interactions between microstructural and device lengthscales.

We will discuss two problems motivated by this setting.
In the first problem, we apply the recent peridynamic theory of continuum mechanics to the problem of dynamic propagation of a martensitic phase boundary.
Peridynamics is a continuum formulation that works directly with the displacement field, providing some freedom from tracking discontinuities, as well as incorporating long-range effects that can be important at small scales.
Our study of martensitic interfaces in the peridynamic framework suggests that the theory is closed with respect to kinetics and nucleation and does not require additional information as in classical continuum mechanics.
In particular, kinetics can be understood in the framework of traveling waves, and nucleation as a dynamic linear instability.
Further, the computational ease of the theory allows us to examine the interaction between a phase boundary and an inclusion
In the second problem, we examine the problem of long-range electric fields in ferroelectric crystals. Ferroelectrics in current devices are fabricated with complex geometries, and predicting the microstructure in these geometries is challenging due to the presence of long-range electric fields.
We present a mesoscale model of ferroelectric crystals and a method that exploits boundary elements and Dirichlet-to-Neumann maps to solve this model.
We also discuss some calculations of the complex microstructure that arises due to the interactions between mechanics and long-range electrostatics.




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