Zusammenfassung für den Vortrag am 18.12.2019 (11:00 Uhr)

Arbeitsgemeinschaft ANGEWANDTE ANALYSIS

Lauro Morales (Universidad Nacional Autónoma de México)
Some Results on quasiconvex hull for a n-well problem in 2D under Geometrically Linear Elastic regime

In shape-memory alloys, it is common to analyze pattern formation induced by the existence of different zero free energy phases in the material. These microstructure provokes the shape-memory effect. The classical model used to study the problem is

         ∫    inf      ϕ (∇y)dx,  kerϕ = {u,u , ...,u }⊕ ℝ2×2 , y∈W 1,∞ (Ω)  Ω                    1 2      n     skew  y|∂Ω=Fx
(1)

where {u1,u2,,un}⊂ sym2×2 and the function ϕ : 2×2 satisfies mild growth conditions and it is invariant under addition of skew-symmetric matrices to its argument.

In this talk, I will present some recent results about the relaxed problem via quasiconvexification. More precisely, it will be proved that the quasiconvex hull of kerϕ equals its convex hull if the n wells are pairsewise symmetrized-rank-one connected. Particularly, in the three-well problem if one of this connection is lost, then the contention of the quasiconvex hull of kerϕ in its convex hull is strict.

 

20.12.2019, 02:31