TY  - JOUR
A1  - Chenchiah, Isaac
A1  - Schlömerkemper, Anja
T1  - Non-laminate microstructures in monoclinic-I martensite
N2  - We study the symmetrised rank-one convex hull of monoclinic-I martensite (a twelve-variant material) in the context of geometrically-linear elasticity. We construct sets of T3s, which are (non-trivial) symmetrised rank-one convex hulls of 3-tuples of pairwise incompatible strains. Moreover we construct a five-dimensional continuum of T3s and show that its intersection with the boundary of the symmetrised rank-one convex hull is four-dimensional. We also show that there is another kind of monoclinic-I martensite with qualitatively different semi-convex hulls which, so far as we know, has not been experimentally observed. Our strategy is to combine understanding of the algebraic structure of symmetrised rank-one convex cones with knowledge of the faceting structure of the convex polytope formed by the strains.
KW  - Martensit
KW  - Mehrskalenmodell
KW  - Phasenumwandlung
KW  - Variationsrechnung
KW  - kubisch-monokliner Phasenübergang
KW  - semi-konvexe Hüllen
KW  - geometrisch lineare Elastizitätstheorie
KW  - T3s
KW  - cubic-monoclinic martensites
KW  - semi-convex hulls
KW  - geometrically linear elasticity
KW  - T3s
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-72134
ER  - 
TY  - JOUR
A1  - Lauerbach, Laura
A1  - Neukamm, Stefan
A1  - Schäffner, Mathias
A1  - Schlömerkemper, Anja
T1  - Continuum Limit and Homogenization of Stochastic and Periodic Discrete Systems – Fracture in Composite Materials
JF  - Proceedings in Applied Mathematics & Mechanics
N2  - The limiting behaviour of a one‐dimensional discrete system is studied by means of Γ‐convergence. We consider a toy model of a chain of atoms. The interaction potentials are of Lennard‐Jones type and periodically or stochastically distributed. The energy of the system is considered in the discrete to continuum limit, i.e. as the number of atoms tends to infinity. During that limit, a homogenization process takes place. The limiting functional is discussed, especially with regard to fracture. Secondly, we consider a rescaled version of the problem, which yields a limiting energy of Griffith's type consisting of a quadratic integral term and a jump contribution. The periodic case can be found in [8], the stochastic case in [6,7].
KW  - discrete systems
KW  - continuum limit
KW  - homogenization
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-211835
VL  - 19
IS  - 1
ER  - 
TY  - JOUR
A1  - Kalousek, Martin
A1  - Mitra, Sourav
A1  - Schlömerkemper, Anja
T1  - Existence of weak solutions of diffuse interface models for magnetic fluids
JF  - Proceedings in Applied Mathematics and Mechanics
N2  - In this article we collect some recent results on the global existence of weak solutions for diffuse interface models involving incompressible magnetic fluids. We consider both the cases of matched and unmatched specific densities. For the model involving fluids with identical densities we consider the free energy density to be a double well potential whereas for the unmatched density case it is crucial to work with a singular free energy density.
KW  - mathematics
KW  - magnetic fluids
KW  - diffuse interface models
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-257642
VL  - 21
IS  - 1
ER  -