20 citations · 39 across the 7 of their papers we have counts for
11 papers
Dimension reduction for a coupled electro-elastic saddle-point problem at finite strains
Kateryna Buryachenko, Annegret Glitzky, Matthias Liero +1
We study the finite deformation of a thin, elastically heterogeneous sheet subject to electrostatic coupling. The interaction between mechanics and electrostatics is formulated as…
Derivation of the Reissner-Mindlin model from nonlinear elasticity
Tamara Fastovska, Janusz Ginster, Barbara Zwicknagl
We discuss how the Reissner-Mindlin plate model can be derived from three-dimensional finite elasticity in terms of -convergence. The presence of transverse shear effects in the…
Microstructures in a two-dimensional frustrated spin system: Scaling regimes and a discrete-to-continuum limit
Janusz Ginster, Melanie Koser, Barbara Zwicknagl
We study pattern formation within the - - spin model on a two-dimensional square lattice in the case of incompatible (ferromagnetic) boundary conditions on the spin field…
On the Effect of Geometry on Scaling Laws for a Class of Martensitic Phase Transformations
Janusz Ginster, Angkana Rüland, Antonio Tribuzio +1
We study scaling laws for singular perturbation problems associated with a class of two-dimensional martensitic phase transformations and deduce a domain dependence of the scaling…
Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys
Sergio Conti, Johannes Diermeier, David Melching +1
We consider a singularly-perturbed two-well problem in the context of planar geometrically linear elasticity to model a rectangular martensitic nucleus in an austenitic matrix. We…
Geometry of martensite needles in shape memory alloys
Sergio Conti, Martin Lenz, Nora Lüthen +2
We study the geometry of needle-shaped domains in shape-memory alloys. Needle-shaped domains are ubiquitously found in martensites around macroscopic interfaces between regions whi…
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,…
Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in
Angkana Rüland, Christian Zillinger, Barbara Zwicknagl
In this article we continue our study of higher Sobolev regularity of flexible convex integration solutions to differential inclusions arising from applications in materials scienc…
Higher Sobolev Regularity of Convex Integration Solutions in Elasticity
Angkana Rüland, Christian Zillinger, Barbara Zwicknagl
In this article we discuss quantitative properties of convex integration solutions arising in problems modeling shape-memory materials. For a two-dimensional, geometrically lineari…
Deformation concentration for martensitic microstructures in the limit of low volume fraction
Sergio Conti, Johannes Diermeier, Barbara Zwicknagl
We consider a singularly-perturbed nonconvex energy functional which arises in the study of microstructures in shape memory alloys. The scaling law for the minimal energy predicts…
Low volume-fraction microstructures in martensites and crystal plasticity
Sergio Conti, Barbara Zwicknagl
We study microstructure formation in two nonconvex singularly-perturbed variational problems from materials science, one modeling austenite-martensite interfaces in shape-memory al…