相关论文: Rigidity of branching microstructures in shape mem…

We study the branching of twins appearing in shape memory alloys at the interface between austenite and martensite. In the framework of three-dimensional non-linear elasticity theory, we propose an explicit, low-energy construction of the…

We develop a 1D model of twin branching in shape memory alloys. The free energy of the branched microstructure comprises the interfacial and elastic strain energy contributions, both expressed in terms of the average twin spacing treated as…

Needle-like twins are observed experimentally within the transition layer at the martensite-twinned martensite interface. We utilize a phase-field approach to investigate this microstructure. Our goal is to simulate the morphology of the…

Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and M\"uller studied a branching pattern with optimal scaling of the energy with respect to its parameters.…

In this paper we introduce a 3D phenomenological model for shape memory behavior, accounting for: martensite reorientation, asymmetric response of the material to tension/compression, different kinetics between forward and reverse phase…

A sharp-interface model describing static equilibrium configurations of shape mory alloys by means of interfacial polyconvex energy density introduced by \v{S}ilhav\'y in 2010 and extended to a quasistatic situation by Kn\"upfer and…

We quantify the rigidity of branching microstructures in shape memory alloys undergoing cubic-to-tetragonal transformations in the geometrically linearized theory by making use of Tartar's H-measures. The main result is a…

We use the phase-field method to study the martensitic transformation at the nanoscale. For nanosystems such as nanowires and nanograins embedded in a stiff matrix, the geometric constraints and boundary conditions have an impact on…

The paper investigates two-phase microstructures of optimal 3D composites that store minimal elastic energy in a given strain field. The composite is made of two linear isotropic materials which differ in elastic moduli and self-strains. We…

Motivated by experimental observations of H. Seiner et al., we study the nucleation of austenite in a single crystal of a CuAlNi shape-memory alloy stabilized as a single variant of martensite. In the experiments the nucleation process was…

We study energy scaling laws for a simplified, singularly perturbed, double-well nucleation problem confined in a half-space, in the absence of gauge invariance and for an inclusion of fixed volume. Motivated by models for boundary…

Modulated martensites play an important role in magnetic shape memory alloys, because all functional properties are closely connected to the twin microstructure and the phase boundary. The nature of the modulated martensites is still…

NiTi is the most used shape-memory alloy, nonetheless, a lack of understanding remains regarding the associated structures and transitions, including their barriers. Using a generalized solid-state nudge elastic band (GSSNEB) method…

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…

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region…

Domain branching near the boundary appears in many singularly-perturbed models for microstructure in materials and was first demonstrated mathematically by Kohn and M\"uller for a scalar problem modeling the elastic behavior of shape-memory…

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 derive the scaling regimes for the minimal energy in terms…

Three sets of Co-Ni-Ga alloy nanoparticles have been synthesized by a template-free chemical route. Structural, morphological, shape memory, and magnetic properties of room temperature martensite (M) phase, dual (M + secondary $\gamma$)…

We show the existence of an energetic solution to a quasistatic evolutionary model of shape memory alloys. Elastic behavior of each material phase/variant is described by polyconvex energy density. Additionally, to every phase boundary,…

We study the occurrence of domain branching in a class of $(d+1)$-dimensional sharp interface models featuring the competition between an interfacial energy and a non-local field energy. Our motivation comes from branching in uniaxial…