5 papers
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…
On the cofactor conditions and further conditions of supercompatibility between phases
Francesco Della Porta
In this paper we improve the understanding of the cofactor conditions, which are particular conditions of geometric compatibility between austenite and martensite, that are believe…