17 citations · 52 across the 21 of their papers we have counts for
24 papers
Local boundary conditions in nonlocal hyperelasticity via heterogeneous horizons
Carolin Kreisbeck, Hidde Schönberger
In this paper, we consider a class of variational problems with integral functionals involving nonlocal gradients. These models have been recently proposed as refinements of classi…
-convergence involving nonlocal gradients with varying horizon: Recovery of local and fractional models
Javier Cueto, Carolin Kreisbeck, Hidde Schönberger
This work revolves around the rigorous asymptotic analysis of models in nonlocal hyperelasticity. The corresponding variational problems involve integral functionals depending on n…
Characterizing BV- and BD-ellipticity for a class of positively 1-homogeneous surface energy densities
Dominik Engl, Carolin Kreisbeck, Marco Morandotti
Lower semicontinuity of surface energies in integral form is known to be equivalent to BV-ellipticity of the surface density. In this paper, we prove that BV-ellipticity coincides…
Non-constant functions with zero nonlocal gradient and their role in nonlocal Neumann-type problems
Carolin Kreisbeck, Hidde Schönberger
This work revolves around properties and applications of functions whose nonlocal gradient, or more precisely, finite-horizon fractional gradient, vanishes. Surprisingly, in contra…
A variational perspective on auxetic metamaterials of checkerboard-type
Wolf-Patrick Düll, Dominik Engl, Carolin Kreisbeck
The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of phy…
A variational theory for integral functionals involving finite-horizon fractional gradients
Javier Cueto, Carolin Kreisbeck, Hidde Schönberger
The center of interest in this work are variational problems with integral functionals depending on special nonlocal gradients. The latter correspond to truncated versions of the R…
Structural changes in nonlocal denoising models arising through bi-level parameter learning
Elisa Davoli, Rita Ferreira, Carolin Kreisbeck +1
We introduce a unified framework based on bi-level optimization schemes to deal with parameter learning in the context of image processing. The goal is to identify the optimal regu…
Cartesian convexity as the key notion in the variational existence theory for nonlocal supremal functionals
Carolin Kreisbeck, Antonella Ritorto, Elvira Zappale
Motivated by the direct method in the calculus of variations in , our main result identifies the notion of convexity characterizing the weakly lower semicontinuity…
On the interplay of anisotropy and geometry for polycrystals in single-slip crystal plasticity
Dominik Engl, Carolin Kreisbeck
In this paper, we investigate a variational polycrystalline model in finite crystal plasticity with one active slip system and rigid elasticity. The task is to determine inner and…
On static and evolutionary homogenization in crystal plasticity for stratified composites
Elisa Davoli, Carolin Kreisbeck
The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck…
Asymptotic analysis of deformation behavior in high-contrast fiber-reinforced materials: Rigidity and anisotropy
Dominik Engl, Carolin Kreisbeck, Antonella Ritorto
We identify the restricted class of attainable effective deformations in a model of reinforced composites with parallel, long, and fully rigid fibers embedded in an elastic body. I…
Quasiconvexity in the fractional calculus of variations: Characterization of lower semicontinuity and relaxation
Carolin Kreisbeck, Hidde Schönberger
Based on recent developments in the theory of fractional Sobolev spaces, an interesting new class of nonlocal variational problems has emerged in the literature. These problems, wh…
Theories for incompressible rods: a rigorous derivation via -convergence
Dominik Engl, Carolin Kreisbeck
We use variational convergence to derive a hierarchy of one-dimensional rod theories, starting out from three-dimensional models in nonlinear elasticity subject to local volume-pre…
Asymptotic variational analysis of incompressible elastic strings
Dominik Engl, Carolin Kreisbeck
Starting from three-dimensional nonlinear elasticity under the restriction of incompressibility, we derive reduced models to capture the behavior of strings in response to external…
Loss of double-integral character during relaxation
Carolin Kreisbeck, Elvira Zappale
We provide explicit examples to show that the relaxation of functionals where is…
Lower semicontinuity and relaxation of nonlocal -functionals
Carolin Kreisbeck, Elvira Zappale
We study variational problems involving nonlocal supremal functionals where $Ω\subset \mat…
Homogenization in of a model for layered composites in finite crystal plasticity
Elisa Davoli, Rita Ferreira, Carolin Kreisbeck
In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider…
Asymptotic rigidity of layered structures and its application in homogenization theory
Fabian Christowiak, Carolin Kreisbeck
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity,…
Characterizations of symmetric polyconvexity
Omar Boussaid, Carolin Kreisbeck, Anja Schlömerkemper
Symmetric quasiconvexity plays a key role for energy minimization in geometrically linear elasticity theory. Due to the complexity of this notion, a common approach is to retreat t…
Homogenization of layered materials with rigid components in single-slip finite crystal plasticity
Fabian Christowiak, Carolin Kreisbeck
We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two typ…
Heterogeneous thin films: Combining homogenization and dimension reduction with directors
Carolin Kreisbeck, Stefan Krömer
We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with…
Asymptotic spectral analysis in semiconductor nanowire heterostructures
Carolin Kreisbeck, Luísa Mascarenhas
Mathematical settings in which heterogeneous structures affect electron transport through a tube-shaped quantum waveguide are studied, highlighting the interaction between heteroge…
Another approach to the thin-film Gamma-limit of the micromagnetic free energy in the regime of small samples
Carolin Kreisbeck
The asymptotic behavior of the micromagnetic free energy governing a ferromagnetic film is studied as its thickness gets smaller and smaller compared to its cross section. Here the…
Thin-film limits of functionals on A-free vector fields
Carolin Kreisbeck, Filip Rindler
This paper deals with variational principles on thin films subject to linear PDE constraints represented by a constant-rank operator . We study the effective behavior…