Related papers: On Rigidity for the Four-Well Problem Arising in t…
We study a simplified two-dimensional model for a cubic-to-orthorhombic phase transition occuring in certain shape-memory-alloys. In the low temperature regime the linear theory of elasticity predicts various possible patterns of martensite…
We establish a quantitative rigidity estimate for two-well frame-indifferent nonlinear energies, in the case in which the two wells have exactly one rank-one connection. Building upon this novel rigidity result, we then analyze solid-solid…
We consider a two-dimensional problem in nonlinear elasticity which corresponds to the cubic-to-tetragonal phase transformation. Our model is frame invariant and the energy density is given by the squared distance from two potential wells.…
We show how the St.Venant compatibility relations for strain in three dimensions lead to twinning for the cubic to tetragonal transition in martensitic materials within a Ginzburg-Landau model in terms of the six components of the symmetric…
Composed of square particles, the tetratic phase is characterised by a four-fold symmetry with quasi-long-range orientational order but no translational order. We construct the elastic free energy for tetratics and find a closed form…
We study geometrical clues of a rigidity transition due to the emergence of a system-spanning state of self stress in under-constrained systems of individual polygons and spring networks constructed from such polygons. When a polygon with…
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, planar $n$-well problem, generalising results of [CKZ17].…
In this paper we consider nonlinearly elastic, frame-indifferent, and singularly perturbed two-well models for materials undergoing solid-solid phase transitions in any space dimensions, and we perform a simultaneous passage to…
We study equilibrium properties of a system of particles in two dimensions, interacting with pair and three body potentials, which undergoes a structural transition from a square to a rhombic lattice and thus constitutes a simple model for…
We address three related problems in the theory of elasticity, formulated in the framework of double forms: the Saint-Venant compatibility condition, the existence and uniqueness of solutions for equations arising in incompatible…
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…
We formulate a phenomenological elasto-plastic theory to describe a solid undergoing a structural transition from a square (p4mm) to an oblique (p2) lattice in two dimensions. Within our theory, the components of the strain may be…
In this note we combine the "spin-argument" from [KLR15] and the $n$-dimensional incompatible, one-well rigidity result from [LL16], in order to infer a new proof for the compactness of discrete multi-well energies associated with the…
In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for…
We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic…
We consider a sharp interface kinetic model of phase transitions accompanied by elastic strain, together with its phase-field realization. Quantitative results for the steady-state growth of a new phase in a strip geometry are obtained and…
We develop a rigidity theory for frameworks in $\mathbb{R}^3$ which have two coincident points but are otherwise generic and only infinitesimal motions which are tangential to a family of cylinders induced by the realisation are considered.…
The stiff problem is concerned with a thermal conduction model with a singular barrier of zero volume. In this paper, we shall build the phase transitions for the stiff problems in one-dimensional space. It turns out that every phase…
The application of stress to multiphase solid-liquid systems often results in morphological instabilities. Here we propose a solid-solid phase transformation model for roughening instability in the interface between two porous materials…
In this paper we investigate the deformation of cylindrical linearly elastic shells using the Koiter model. We formulate and solve the relaxed Saint-Venant's problem for thin cylindrical tubes made of isotropic and homogeneous elastic…