4 papers · 1 filter
Convex Integration Solutions for the Geometrically Non-linear Two-Well Problem with Higher Sobolev Regularity
Francesco Della Porta, Angkana Rüland
In this article we discuss higher Sobolev regularity of convex integration solutions for the geometrically non-linear two-well problem. More precisely, we construct solutions to th…
Exact constructions in the (non-linear) planar theory of elasticity: From elastic crystals to nematic elastomers
Pierluigi Cesana, Francesco Della Porta, Angkana Rüland +2
In this article we deduce necessary and sufficient conditions for the presence of `Conti-type', highly symmetric, exactly-stress free constructions in the geometrically non-linear,…
Interfacial energy as a selection mechanism for minimizing gradient Young measures in a one-dimensional model problem
Francesco Della Porta
Energy functionals describing phase transitions in crystalline solids are often non-quasiconvex and minimizers might therefore not exist. On the other hand, there might be infinite…
A model for the evolution of highly reversible martensitic transformations
Francesco Della Porta
In this work we introduce a new system of partial differential equations as a simplified model for the evolution of reversible martensitic transformations under thermal cycling in…