Analysis Seminar

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Variational derivation of surface tension for grain boundary in crystals

Speaker: Adriana Garroni, Universita di Roma ``La Sapienza''

Location: Warren Weaver Hall 1302

Date: Thursday, September 15, 2022, 11 a.m.

Synopsis:

We derive, via Gamma convergence, a surface tension model for
polycrystals in dimension two. The starting point is a semi-discrete
model accounting for the possibility of having crystal defects proposed
by Lauteri and Luckhaus. The presence of defects is modelled by
incompatible strain fields with quantised curl. In the limit as the
lattice spacing tends to zero we obtain an energy for grain boundaries
that depends on the relative angle of the orientations of the two
neighbouring grains. The energy density is defined through an asymptotic
cell problem formula. By means of the bounds obtained by Lauteri and
Luckhaus we also show that the energy density exhibits a logarithmic
behaviour for small angle grain boundaries in agreement with the
classical Read Shockley formula.

This is joint work with Emanuele
Spadaro.